# Showing papers in "IEEE Transactions on Automatic Control in 2007"

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TL;DR: This note investigates a simple event-triggered scheduler based on the paradigm that a real-time scheduler could be regarded as a feedback controller that decides which task is executed at any given instant and shows how it leads to guaranteed performance thus relaxing the more traditional periodic execution requirements.

Abstract: In this note, we revisit the problem of scheduling stabilizing control tasks on embedded processors. We start from the paradigm that a real-time scheduler could be regarded as a feedback controller that decides which task is executed at any given instant. This controller has for objective guaranteeing that (control unrelated) software tasks meet their deadlines and that stabilizing control tasks asymptotically stabilize the plant. We investigate a simple event-triggered scheduler based on this feedback paradigm and show how it leads to guaranteed performance thus relaxing the more traditional periodic execution requirements.

2,850 citations

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TL;DR: The main result shows that when beta<1/2 convergence of the flock to a common velocity is guaranteed, while for betages1/ 2 convergence is guaranteed under some condition on the initial positions and velocities of the birds only.

Abstract: We provide a model (for both continuous and discrete time) describing the evolution of a flock. Our model is parameterized by a constant beta capturing the rate of decay-which in our model is polynomial-of the influence between birds in the flock as they separate in space. Our main result shows that when beta<1/2 convergence of the flock to a common velocity is guaranteed, while for betages1/2 convergence is guaranteed under some condition on the initial positions and velocities of the birds only

1,377 citations

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TL;DR: In this article, the stability properties of a group of mobile agents that align their velocity vectors, and stabilize their inter-agent distances, using decentralized, nearest-neighbor interaction rules, exchanging information over networks that change arbitrarily (no dwell time between consecutive switches).

Abstract: This note analyzes the stability properties of a group of mobile agents that align their velocity vectors, and stabilize their inter-agent distances, using decentralized, nearest-neighbor interaction rules, exchanging information over networks that change arbitrarily (no dwell time between consecutive switches). These changes introduce discontinuities in the agent control laws. To accommodate for arbitrary switching in the topology of the network of agent interactions we employ nonsmooth analysis. The main result is that regardless of switching, convergence to a common velocity vector and stabilization of inter-agent distances is still guaranteed as long as the network remains connected at all times

1,242 citations

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TL;DR: A state aggregation technique is developed to obtain a set of decentralized control laws for the individuals which possesses an epsiv-Nash equilibrium property and a stability property of the mass behavior is established.

Abstract: We consider linear quadratic Gaussian (LQG) games in large population systems where the agents evolve according to nonuniform dynamics and are coupled via their individual costs. A state aggregation technique is developed to obtain a set of decentralized control laws for the individuals which possesses an epsiv-Nash equilibrium property. A stability property of the mass behavior is established, and the effect of inaccurate population statistics on an isolated agent is also analyzed by variational techniques.

855 citations

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TL;DR: A passivity-based design framework is developed, which results in a broad class of feedback rules that encompass as special cases some of the existing formation stabilization and group agreement designs in the literature.

Abstract: We pursue a group coordination problem where the objective is to steer the differences between output variables of the group members to a prescribed compact set. To stabilize this set we study a class of feedback rules that are implementable with local information available to each member. When the information flow between neighboring members is bidirectional, we show that the closed-loop system exhibits a special interconnection structure which inherits the passivity properties of its components. By exploiting this structure we develop a passivity-based design framework, which results in a broad class of feedback rules that encompass as special cases some of the existing formation stabilization and group agreement designs in the literature. The passivity approach offers additional design flexibility compared to these special cases, and systematically constructs a Lurie-type Lyapunov function for the closed-loop system. We further study the robustness of these feedback laws in the presence of a time-varying communication topology, and present a persistency of excitation condition which allows the interconnection graph to lose connectivity pointwise in time as long as it is established in an integral sense.

750 citations

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TL;DR: A novel method is proposed in this note for stability analysis of systems with a time-varying delay by considering the additional useful terms when estimating the upper bound of the derivative of Lyapunov functionals and introducing the new free-weighting matrices.

Abstract: A novel method is proposed in this note for stability analysis of systems with a time-varying delay. Appropriate Lyapunov functional and augmented Lyapunov functional are introduced to establish some improved delay-dependent stability criteria. Less conservative results are obtained by considering the additional useful terms (which are ignored in previous methods) when estimating the upper bound of the derivative of Lyapunov functionals and introducing the new free-weighting matrices. The resulting criteria are extended to the stability analysis for uncertain systems with time-varying structured uncertainties and polytopic-type uncertainties. Numerical examples are given to demonstrate the effectiveness and the benefits of the proposed method

710 citations

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TL;DR: It is demonstrated how adaptive switching supervisory control can be combined with a nonlinear Lyapunov-based tracking control law to solve the problem of global boundedness and convergence of the position tracking error to a neighborhood of the origin that can be made arbitrarily small.

Abstract: We address the problem of position trajectory-tracking and path-following control design for underactuated autonomous vehicles in the presence of possibly large modeling parametric uncertainty. For a general class of vehicles moving in either 2- or 3-D space, we demonstrate how adaptive switching supervisory control can be combined with a nonlinear Lyapunov-based tracking control law to solve the problem of global boundedness and convergence of the position tracking error to a neighborhood of the origin that can be made arbitrarily small. The desired trajectory does not need to be of a particular type (e.g., trimming trajectories) and can be any sufficiently smooth bounded curve parameterized by time. We also show how these results can be applied to solve the path-following problem, in which the vehicle is required to converge to and follow a path, without a specific temporal specification. We illustrate our design procedures through two vehicle control applications: a hovercraft (moving on a planar surface) and an underwater vehicle (moving in 3-D space). Simulations results are presented and discussed.

706 citations

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TL;DR: Several new conditions are obtained for the asymptotic stability of discrete-time systems with time-varying state delay by defining new Lyapunov functions and by making use of novel techniques to achieve delay dependence.

Abstract: This note is concerned with the stability analysis of discrete-time systems with time-varying state delay. By defining new Lyapunov functions and by making use of novel techniques to achieve delay dependence, several new conditions are obtained for the asymptotic stability of these systems. The merit of the proposed conditions lies in their less conservativeness, which is achieved by circumventing the utilization of some bounding inequalities for cross products between two vectors and by paying careful attention to the subtle difference between the terms Sigmam=k-dk k-1(middot) and Sigma m=k-dM k-1(middot), which is largely ignored in the existing literature. These conditions are shown, via several examples, to be much less conservative than some existing result

647 citations

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TL;DR: This paper proposes a parameter-dependent filter design procedure, which is much less conservative than the quadratic approach and provides alternatives for designing robust Hinfin filters with different degrees of conservativeness and computational complexity.

Abstract: This paper investigates the problem of robust Hinfin estimation for uncertain systems subject to limited communication capacity The parameter uncertainty belongs to a given convex polytope and the communication limitations include measurement quantization, signal transmission delay, and data packet dropout, which appear typically in a network environment The problem of Hinfin filter design is first solved for a nominal system subject to the aforementioned information limitations, which is then extended to the uncertain case based on the notion of quadratic stability To further reduce the overdesign in the quadratic framework, this paper also proposes a parameter-dependent filter design procedure, which is much less conservative than the quadratic approach The quadratic and parameter-dependent approaches provide alternatives for designing robust Hinfin filters with different degrees of conservativeness and computational complexity Two examples, including a mass-spring system, are utilized to illustrate the design procedures proposed in this paper

552 citations

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TL;DR: The results of the paper provide a low-order parametric family of stabilizable collectives that offer a set of primitives for the design of higher-level tasks at the group level.

Abstract: This paper proposes a design methodology to stabilize isolated relative equilibria in a model of all-to-all coupled identical particles moving in the plane at unit speed. Isolated relative equilibria correspond to either parallel motion of all particles with fixed relative spacing or to circular motion of all particles with fixed relative phases. The stabilizing feedbacks derive from Lyapunov functions that prove exponential stability and suggest almost global convergence properties. The results of the paper provide a low-order parametric family of stabilizable collectives that offer a set of primitives for the design of higher-level tasks at the group level

490 citations

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TL;DR: A decentralized feedback control strategy that drives a system of multiple nonholonomic unicycles to a rendezvous point in terms of both position and orientation is introduced.

Abstract: In this note, a decentralized feedback control strategy that drives a system of multiple nonholonomic unicycles to a rendezvous point in terms of both position and orientation is introduced. The proposed nonholonomic control law is discontinuous and time-invariant and using tools from nonsmooth Lyapunov theory and graph theory the stability of the overall system is examined. Similarly to the linear case, the convergence of the multi-agent system relies on the connectivity of the communication graph that represents the inter-agent communication topology. The control law is first defined in order to guarantee connectivity maintenance for an initially connected communication graph. Moreover, the cases of static and dynamic communication topologies are treated as corollaries of the proposed framework

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TL;DR: New NCS models are provided considering both single- and multiple-packet transmissions and sufficient conditions for stochastic stability are derived in the form of linear matrix inequalities (LMIs) and corresponding control laws are given.

Abstract: This note is concerned with stability and controller design of networked control systems (NCSs) with packet dropouts. New NCS models are provided considering both single- and multiple-packet transmissions. Both sensor-to-controller (S/C) and controller-to-actuator (C/A) packet dropouts are modeled and their history behavior is described by different independent Markov chains. In term of the given models, sufficient conditions for stochastic stability are derived in the form of linear matrix inequalities (LMIs) and corresponding control laws are given. Numerical examples illustrate the effectiveness of the results.

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TL;DR: In this paper, a hierarchy of approximation pseudo-metrics between two systems is defined to quantify the quality of the approximation, and the established exact relationships are captured as zero sections.

Abstract: Established system relationships for discrete systems, such as language inclusion, simulation, and bisimulation, require system observations to be identical. When interacting with the physical world, modeled by continuous or hybrid systems, exact relationships are restrictive and not robust. In this paper, we develop the first framework of system approximation that applies to both discrete and continuous systems by developing notions of approximate language inclusion, approximate simulation, and approximate bisimulation relations. We define a hierarchy of approximation pseudo-metrics between two systems that quantify the quality of the approximation, and capture the established exact relationships as zero sections. Our approximation framework is compositional for a synchronous composition operator. Algorithms are developed for computing the proposed pseudo-metrics, both exactly and approximately. The exact algorithms require the generalization of the fixed point algorithms for computing simulation and bisimulation relations, or dually, the solution of a static game whose cost is the so-called branching distance between the systems. Approximations for the pseudo-metrics can be obtained by considering Lyapunov-like functions called simulation and bisimulation functions. We illustrate our approximation framework in reducing the complexity of safety verification problems for both deterministic and nondeterministic continuous systems

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TL;DR: This paper considers the application of the unscented Kalman filter (UKF) to continuous-time filtering problems, where both the state and measurement processes are modeled as stochastic differential equations.

Abstract: This paper considers the application of the unscented Kalman filter (UKF) to continuous-time filtering problems, where both the state and measurement processes are modeled as stochastic differential equations. The mean and covariance differential equations which result in the continuous-time limit of the UKF are derived. The continuous-discrete UKF is derived as a special case of the continuous-time filter, when the continuous-time prediction equations are combined with the update step of the discrete-time UKF. The filter equations are also transformed into sigma-point differential equations, which can be interpreted as matrix square root versions of the filter equations.

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TL;DR: This note addresses a coordination problem of a multiagent system with jointly connected interconnection topologies with neighbor-based rules to realize local control strategies for these continuous-time autonomous agents described by double integrators.

Abstract: This note addresses a coordination problem of a multiagent system with jointly connected interconnection topologies. Neighbor-based rules are adopted to realize local control strategies for these continuous-time autonomous agents described by double integrators. Although the interagent connection structures vary over time and related graphs may not be connected, a sufficient condition to make all the agents converge to a common value is given for the problem by a proposed Lyapunov-based approach and related space decomposition technique

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TL;DR: This paper presents a methodology for safety verification of continuous and hybrid systems in the worst-case and stochastic settings, and computes an upper bound on the probability that a trajectory of the system reaches the unsafe set, a bound whose validity is proven by the existence of a barrier certificate.

Abstract: This paper presents a methodology for safety verification of continuous and hybrid systems in the worst-case and stochastic settings. In the worst-case setting, a function of state termed barrier certificate is used to certify that all trajectories of the system starting from a given initial set do not enter an unsafe region. No explicit computation of reachable sets is required in the construction of barrier certificates, which makes it possible to handle nonlinearity, uncertainty, and constraints directly within this framework. In the stochastic setting, our method computes an upper bound on the probability that a trajectory of the system reaches the unsafe set, a bound whose validity is proven by the existence of a barrier certificate. For polynomial systems, barrier certificates can be constructed using convex optimization, and hence the method is computationally tractable. Some examples are provided to illustrate the use of the method.

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TL;DR: The method proposed can be applied to determine homogeneous parameter-dependent matrix solutions to a wide variety of PD-LMIs by transforming the infinite-dimensional LMI problem described in terms of uncertain parameters belonging to the unit simplex in a sequence of finite- dimensional LMI conditions which converges to the necessary conditions for the existence of a homogeneous polynomially parameter- dependent solution of arbitrary degree.

Abstract: This note investigates the robust stability of uncertain linear time-invariant systems in polytopic domains by means of parameter-dependent linear matrix inequality (PD-LMI) conditions, exploiting some algebraic properties provided by the uncertainty representation. A systematic procedure to construct a family of finite-dimensional LMI relaxations is provided. The robust stability is assessed by means of the existence of a Lyapunov function, more specifically, a homogeneous polynomially parameter-dependent Lyapunov (HPPDL) function of arbitrary degree. For a given degree , if an HPPDL solution exists, a sequence of relaxations based on real algebraic properties provides sufficient LMI conditions of increasing precision and constant number of decision variables for the existence of an HPPDL function which tend to the necessity. Alternatively, if an HPPDL solution of degree exists, a sequence of relaxations which increases the number of variables and the number of LMIs will provide an HPPDL solution of larger degree. The method proposed can be applied to determine homogeneous parameter-dependent matrix solutions to a wide variety of PD-LMIs by transforming the infinite-dimensional LMI problem described in terms of uncertain parameters belonging to the unit simplex in a sequence of finite-dimensional LMI conditions which converges to the necessary conditions for the existence of a homogeneous polynomially parameter-dependent solution of arbitrary degree. Illustrative examples show the efficacy of the proposed conditions when compared with other methods from the literature.

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TL;DR: This work presents a necessary and sufficient condition for the existence of a common linear copositive Lyapunov function existence for switched systems with two constituent linear time-invariant systems.

Abstract: We consider the problem of common linear copositive Lyapunov function existence for positive switched linear systems. In particular, we present a necessary and sufficient condition for the existence of such a function for switched systems with two constituent linear time-invariant systems. Several applications of this result are also given.

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TL;DR: This work discusses both continuous and discrete time cases, and shows that for either state feedback, or for output feedback delay-free, minimum phase plants, there are limitations on the ability to stabilize an unstable plant over an SNR constrained channel.

Abstract: There has recently been significant interest in feedback stabilization problems with communication constraints including constraints on the available data rate. Signal-to-noise ratio (SNR) constraints are one way in which data-rate limits arise, and are the focus of this paper. In both continuous and discrete-time settings, we show that there are limitations on the ability to stabilize an unstable plant over a SNR constrained channel using finite-dimensional linear time invariant (LTI) feedback. In the case of state feedback, or output feedback with a delay-free, minimum phase plant, these limitations in fact match precisely those that might have been inferred by considering the associated ideal Shannon capacity data rate over the same channel. In the case of LTI output feedback, additional limitations are shown to apply if the plant is nonminimum phase. In this case, we show that for a continuous-time nonminimum phase plant, a periodic linear time varying feedback scheme with fast sampling may be used to recover the original SNR requirement at the cost of robustness properties. The proposed framework inherently captures channel noise effects in a simple formulation suited to conventional LTI control performance and robustness analysis, and has potential to handle time delays and bandwidth constraints in a variety of control over communication links problems.

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İnönü University

^{1}TL;DR: An algorithm based on determining a set of global stability regions corresponding to the fractional orders lambda and mu in the range of (0, 2) and choosing the biggest global stability region in this set is presented.

Abstract: This technical note presents a solution to the problem of stabilizing a given fractional-order system with time delay using fractional-order PllambdaDmu controllers. It is based on determining a set of global stability regions in the (kp, Ki, Kd)-space corresponding to the fractional orders lambda and mu in the range of (0, 2) and then choosing the biggest global stability region in this set. This method can be also used to find the set of stabilizing controllers that guarantees prespecified gain and phase margin requirements. The algorithm is simple and has reliable result which is illustrated by an example, and, hence, is practically useful in the analysis and design of fractional-order control systems.

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TL;DR: A systematic approach to the chattering analysis in systems with second-order sliding modes is developed, finding sufficient conditions for the existence of orbitally stable periodic motions in terms of the properties of corresponding Poincare maps.

Abstract: A systematic approach to the chattering analysis in systems with second-order sliding modes is developed. The neglected actuator dynamics is considered to be the main cause of chattering in real systems. The magnitude of oscillations in nonlinear systems with unmodeled fast nonlinear actuators driven by second-order sliding-mode control generalized suboptimal (2-SMC G-SO) algorithms is evaluated. Sufficient conditions for the existence of orbitally stable periodic motions are found in terms of the properties of corresponding Poincare maps. For linear systems driven by 2-SMC G-SO algorithms, analysis tools based on the frequency-domain methods are developed. The first of these techniques is based on the describing function method and provides for a simple approximate approach to evaluate the frequency and the amplitude of possible periodic motions. The second technique represents a modified Tsypkin's method and provides for a relatively simple, theoretically exact, approach to evaluate the periodic motion parameters. Examples of analysis and simulation results are given throughout this paper.

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TL;DR: This note shows that the Hurwitz stability of the convex hull of a set of Metzler matrices is a necessary and sufficient condition for the asymptotic stability for the associated switched linear system under arbitrary switching.

Abstract: It was recently conjectured that the Hurwitz stability of the convex hull of a set of Metzler matrices is a necessary and sufficient condition for the asymptotic stability of the associated switched linear system under arbitrary switching. In this note, we show that (1) this conjecture is true for systems constructed from a pair of second-order Metzler matrices; (2) the conjecture is true for systems constructed from an arbitrary finite number of second-order Metzler matrices; and (3) the conjecture is in general false for higher order systems. The implications of our results, both for the design of switched positive linear systems, and for research directions that arise as a result of our work, are discussed toward the end of the note.

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TL;DR: A distributed RHC algorithm is presented for dynamically coupled nonlinear systems that are subject to decoupled input constraints and the theoretical conditions for feasibility and stability are shown to be satisfied for a set of coupled Van der Pol oscillators that model a walking robot experiment.

Abstract: This paper considers the problem of distributed control of dynamically coupled nonlinear systems that are subject to decoupled constraints. Examples of such systems include certain large scale process control systems, chains of coupled oscillators and supply chain management systems. Receding horizon control (RHC) is a method of choice in these venues as constraints can be explicitly accommodated. In addition, a distributed control approach is sought to enable the autonomy of the individual subsystems and reduce the computational burden of centralized implementations. In this paper, a distributed RHC algorithm is presented for dynamically coupled nonlinear systems that are subject to decoupled input constraints. By this algorithm, each subsystem computes its own control locally. Provided an initially feasible solution can be found, subsequent feasibility of the algorithm is guaranteed at every update, and asymptotic stabilization is established. The theoretical conditions for feasibility and stability are shown to be satisfied for a set of coupled Van der Pol oscillators that model a walking robot experiment. In simulations, distributed and centralized receding horizon controllers are employed for stabilization of the oscillators. The numerical experiments show that the controllers perform comparably, while the computational savings of the distributed implementation over the centralized implementation is clearly demonstrated.

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TL;DR: A class of hybrid optimal control problems (HOCP) for systems with controlled and autonomous location transitions is formulated and a set of necessary conditions for hybrid system trajectory optimality is presented which together constitute generalizations of the standard Maximum Principle.

Abstract: A class of hybrid optimal control problems (HOCP) for systems with controlled and autonomous location transitions is formulated and a set of necessary conditions for hybrid system trajectory optimality is presented which together constitute generalizations of the standard Maximum Principle; these are given for the cases of open bounded control value sets and compact control value sets. The derivations in the paper employ: (i) classical variational and needle variation techniques; and (ii) a local controllability condition which is used to establish the adjoint and Hamiltonian jump conditions in the autonomous switching case. Employing the hybrid minimum principle (HMP) necessary conditions, a class of general HMP based algorithms for hybrid systems optimization are presented and analyzed for the autonomous switchings case and the controlled switchings case. Using results from the theory of penalty function methods and Ekeland's variational principle the convergence of these algorithms is established under reasonable assumptions. The efficacy of the proposed algorithms is illustrated via computational examples.

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TL;DR: It is shown that this characterization of oscillators as open systems that satisfy a particular dissipation inequality has implications for the global stability analysis of limit cycle oscillations: i) in isolated oscillators, ii) in interconnections of oscillations, and iii) for theglobal synchrony analysis in interConnections of identical oscillators.

Abstract: This paper employs dissipativity theory for the global analysis of limit cycles in particular dynamical systems of possibly high dimension. Oscillators are regarded as open systems that satisfy a particular dissipation inequality. It is shown that this characterization has implications for the global stability analysis of limit cycle oscillations: i) in isolated oscillators, ii) in interconnections of oscillators, and iii) for the global synchrony analysis in interconnections of identical oscillators

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TL;DR: This paper shows several versions of the (LaSalle's) invariance principle for general hybrid systems, which allows for nonuniqueness of solutions, Zeno behaviors, and does not insist on continuous dependence of solutions on initial conditions.

Abstract: This paper shows several versions of the (LaSalle's) invariance principle for general hybrid systems. The broad framework allows for nonuniqueness of solutions, Zeno behaviors, and does not insist on continuous dependence of solutions on initial conditions. Instead, only a mild structural property involving graphical convergence of solutions is posed. The general invariance results are then specified to hybrid systems given by set-valued data. Further results involving invariance as well as observability, detectability, and asymptotic stability are given.

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TL;DR: The main value of the book is that it us an up-to-date reference of dissipative systems in the framework of many system descriptions, and is a good roadmap to the many contributions on the subject.

Abstract: This book presents a fully revised and expanded treatment of dissipative systems theory. It examines linear and nonlinear systems with examples of both in each chapter; some infinite-dimensional examples are also included. Throughout emphasis is placed on the use of the dissipative properties of a system for the design of stable feedback control laws. This second edition is substantially reorganized both to accommodate new material and to enhance its pedagogical properties. The main value of the book is that it us an up-to-date reference of dissipative systems in the framework of many system descriptions. It is a good roadmap to the many contributions on the subject. It is a good reference for dissipative systems for advanced engineering students and researchers in control, however quantity was obtained at the cost of pedagogical quality; an opportunity was missed to create an interesting textbook for these categories. The text is recommended for its vast amount of timely information and indications to the literature. However, the latter information could have been better filtered and structured to provide a unified basic deep knowledge of the field of dissipative systems, which can be mentally reconstructed by the student reader.

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TL;DR: A systematic framework to exploit alternative decomposition structures as a way to obtain different distributed algorithms, each with a different tradeoff among convergence speed, message passing amount and asymmetry, and distributed computation architecture is presented.

Abstract: Network utility maximization (NUM) problem formulations provide an important approach to conduct network resource allocation and to view layering as optimization decomposition In the existing literature, distributed implementations are typically achieved by means of the so-called dual decomposition technique However, the span of decomposition possibilities includes many other elements that, thus far, have not been fully exploited, such as the use of the primal decomposition technique, the versatile introduction of auxiliary variables, and the potential of multilevel decompositions This paper presents a systematic framework to exploit alternative decomposition structures as a way to obtain different distributed algorithms, each with a different tradeoff among convergence speed, message passing amount and asymmetry, and distributed computation architecture Several specific applications are considered to illustrate the proposed framework, including resource-constrained and direct-control rate allocation, and rate allocation among QoS classes with multipath routing For each of these applications, the associated generalized NUM formulation is first presented, followed by the development of novel alternative decompositions and numerical experiments on the resulting new distributed algorithms A systematic enumeration and comparison of alternative vertical decompositions in the future will help complete a mathematical theory of network architectures

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Virginia Tech

^{1}TL;DR: This work examines the consensus problem for a group of agents that communicate via a stochastic information network that is modeled as a weighted directed random graph that switches periodically.

Abstract: We examine the consensus problem for a group of agents that communicate via a stochastic information network. Communication among agents is modeled as a weighted directed random graph that switches periodically. The existence of any edge is probabilistic and independent from the existence of any other edge. We further allow each edge to be weighted differently. Sufficient conditions for asymptotic almost sure consensus are presented for the case of positive weights and for the case of arbitrary weights.

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TL;DR: This note revises the so-called input delay approach to the control of sampled-data systems with nonuniform sampling, in which the sample-and-hold circuit is embedded into an analog system with time- varying input delay.

Abstract: This note revises the so-called input delay approach to the control of sampled-data systems with nonuniform sampling, in which the sample-and-hold circuit is embedded into an analog system with a time- varying input delay. It is shown that the conservatism in calculating the maximal admissible sampling period is reduced by about 57% if the time- varying delay embedding step is omitted.