Showing papers in "IEEE Transactions on Circuits and Systems I-regular Papers in 2002"

Synchronization in scale-free dynamical networks: robustness and fragility

Abstract: Recently, it has been demonstrated that many large complex networks display a scale-free feature, that is, their connectivity distributions are in the power-law form. In this paper, we investigate the synchronization phenomenon in scale-free dynamical networks. We show that if the coupling strength of a scale-free dynamical network is greater than a positive threshold, then the network will synchronize no matter how large it is. We show that the synchronizability of a scale-free dynamical network is robust against random removal of nodes, but is fragile to specific removal of the most highly connected nodes.

Fast terminal sliding-mode control design for nonlinear dynamical systems

Abstract: A fast terminal dynamics is proposed and used in the design of the sliding-mode control for single-input single-output nonlinear dynamical systems. The inherent dynamic properties of the fast terminal sliding modes are explored and conditions to ensure its applicability for control designs are obtained.

Discretization schemes for fractional-order differentiators and integrators

Abstract: For fractional-order differentiator s/sup r/ where r is a real number, its discretization is a key step in digital implementation. Two discretization methods are presented. The first scheme is a direct recursive discretization of the Tustin operator. The second one is a direct discretization method using the Al-Alaoui operator via continued fraction expansion (CFE). The approximate discretization is minimum phase and stable. Detailed discretization procedures and short MATLAB scripts are given. Examples are included for illustration.

Stability of genetic regulatory networks with time delay

Abstract: Presents a model for genetic regulatory networks with time delays, which is described by functional differential equations or delay differential equations (DDE), provide necessary and sufficient conditions for simplifying the genetic network model, and further analyze nonlinear properties of the model in terms of local stability and bifurcation. The proposed model transforms the original interacting network into several simple transcendental equations at an equilibrium, thereby significantly reducing the computational complexity and making analysis of stability and bifurcation tractable for even large-scale networks. Finally, to test the theory, a repressilator model is used as an example for numerical simulation.

LMI-based approach for asymptotically stability analysis of delayed neural networks

Abstract: This paper derives some sufficient conditions for asymptotic stability of neural networks with constant or time-varying delays. The Lyapunov-Krasovskii stability theory for functional differential equations and the linear matrix inequality (LMI) approach are employed to investigate the problem. It shows how some well-known results can be refined and generalized in a straightforward manner. For the case of constant time delays, the stability criteria are delay-independent; for the case of time-varying delays, the stability criteria are delay-dependent. The results obtained in this paper are less conservative than the ones reported so far in the literature and provides one more set of criteria for determining the stability of delayed neural networks.

A projection neural network and its application to constrained optimization problems

Abstract: In this paper, we present a recurrent neural network for solving the nonlinear projection formulation. It is shown here that the proposed neural network is stable in the sense of Lyapunov and globally convergent, globally asymptotically stable, and globally exponentially stable, respectively under different conditions. Compared with the existing neural network for solving the projection formulation, the proposed neural network has a single-layer structure and is amenable to parallel implementation. Moreover, the proposed neural network has no Lipschitz condition, and, thus can be applied to solve a very broad class of constrained optimization problems that are special cases of the nonlinear projection formulation. Simulation shows that the proposed neural network is effective in solving these constrained optimization problems.

Bifurcations and chaos in a permanent-magnet synchronous motor

Abstract: This brief studies dynamic characteristics of a permanent-magnet synchronous motor (PMSM). The mathematical model of the PMSM is first derived, which is fit for carrying out the bifurcation and chaos analysis. Then, the steady-state characteristics of the system, when subject to constant input voltage and constant external torque, are formulated. Three cases are discussed and, for each case, conditions are derived under which the dynamic characteristics of the system are either of steady-state type, limit cycles or chaotic, thus by properly adjusting some system parameters, the system can exhibit limit cycles (LCs) or chaotic behaviors at will. Finally, computer simulations are presented to verify the existence of strange attractors in the PMSM.

Generalized state-space observers for chaotic synchronization and secure communication

Abstract: In this brief, a simple and useful technique for both synchronization and secure communication of chaotic systems is developed. The proposed approach is based on generalized state space observer design for a class of nonlinear systems. By means of regular transformations we show that asymptotic stability is assured under mild conditions. To show accuracy and high performances of the proposed method, the well-known chaotic Lorentz system will be considered as an illustrative example.

Cryptosystems with discretized chaotic maps

Abstract: Many kinds of chaotic cryptosystems have been proposed. Chaotic systems dissipate information due to orbital instability with positive Lyapunov exponents and ergodicity. If these properties are appropriately utilized, chaotic cryptosystems are supposed to realize high security. However, most of the existing secure communication techniques using chaos do not have enough security. For example, secure communication protocols based on chaos synchronization require robustness which gives useful information to attackers. The cryptosystems based on direct applications of chaotic maps have been weak against linear and differential cryptoanalysis. In this paper, a new kind of chaotic cryptosystem which overcomes these difficulties to some extent is proposed. The cryptosystem is based on a discretization of the skew tent map. We also show some of the desirable properties of the proposed cryptosystem using dynamical characteristics. These properties regarding ciphertext randomness may be closely related to the cryptological security. Our new cryptosystem uses one step to connect the theory of commonly used cryptosystems and dynamical system theory.

Stability analysis of linear time-delay systems subject to input saturation

Abstract: This paper is devoted to stability analysis of linear systems with state delay and input saturation. The domain of attraction resulting from an a priori designed state feedback law is analyzed using Lyapunov-Razumikhin and Lyapunov-Krasovskii functional approach. Both delay-independent and delay-dependent estimation of the domain of attraction are presented using the linear matrix inequality technique. The problem of designing linear state feedback laws such that the domain of attraction is enlarged is formulated and solved as an optimization problem with LMI constraints. Numerical examples are used to demonstrate the effectiveness of the proposed design technique.

Charge-pump circuits: power-consumption optimization

Abstract: In this paper, an optimized strategy for designing charge pumps with minimum power consumption is presented. The approach allows designers to define the number of stages that, for a given input, and an output voltage, maximize power efficiency. Capacitor value is then set to provide the current capability required. This approach was analytically developed and validated through simulations and experimental measurements on 0.35-/spl mu/m EEPROM CMOS technology. This approach was then compared with one which minimized the silicon area and it was shown that only a small increase in area is needed to minimize power consumption.

Phase noise and timing jitter in oscillators with colored-noise sources

Abstract: Phase noise or timing jitter in oscillators is of major concern in wireless and optical communications, being a major contributor to the bit-error rate of communication systems, and creating synchronization problems in other clocked and sampled-data systems. This paper presents the theory and practical characterization of phase noise in oscillators due to colored, as opposed to white, noise sources. Shot and thermal noise sources in oscillators can be modeled as white-noise sources for all practical purposes. The characterization of phase noise in oscillators due to shot and thermal noise sources is covered by a recently developed theory of phase noise due to white-noise sources. The extension of this theory and the practical characterization techniques to noise sources in oscillators, which have a colored spectral density, e.g., 1/f noise, is crucial for practical applications. In this paper, we first derive a stochastic characterization of phase noise in oscillators due to colored-noise sources. This stochastic analysis is based on a novel nonlinear perturbation analysis for autonomous systems, and a nonlocal Fokker-Planck equation we derive. Then, we calculate the resulting spectrum of the oscillator output with phase noise as characterized. We also extend our results to the case when both white and colored-noise sources are present. Our treatment of phase noise due to colored-noise sources is general, i.e., it is not specific to a particular type of colored-noise source.

An improved global stability result for delayed cellular neural networks

Abstract: This paper presents a sufficient condition for the uniqueness and global asymptotic stability of the equilibrium point for delayed cellular neural networks. This result improves and generalizes some of the previous stability results derived in the literature.

Noise analysis of phase-locked loops

Abstract: This work addresses the problem of noise analysis of phase-locked loops (PLLs). The problem is formulated as a stochastic differential equation and is solved in the presence of circuit white noise sources yielding the spectrum of the PLL output. Specifically, the effect of loop filter characteristics, phase-frequency detector, and phase noise of the open-loop voltage-controlled oscillator (VCO) on the PLL output spectrum is quantified. These results are derived using a full nonlinear analysis of the VCO in the feedback loop and cannot be predicted using traditional linear analyses or the phase noise analysis of open-loop oscillators. The computed spectrum matches well with measured results; specifically, the shape of the output spectrum matches very well with measured PLL output spectra reported in the literature for different kinds of loop filters and phase detectors. The PLL output spectrum computation only requires the phase noise of the VCO, loop filter and phase detector noise, phase detector gain, and loop filter transfer function and does not require the transient simulation of the entire PLL which can be very expensive. The noise analysis technique is illustrated with some examples.

Simple learning control made practical by zero-phase filtering: applications to robotics

Abstract: Iterative learning control (ILC) applies to control systems that perform the same finite-time tracking command repeatedly. It iteratively adjusts the command from one repetition to the next in order to reduce the tracking error. This creates a two-dimensional (2-D) system, with time step and repetition number as independent variables. The simplest form of ILC uses only one gain times one error in the previous repetition, and can be shown to converge to the zero-tracking error independent of the system dynamics. Hence, it appears very effective from a mathematical perspective. However, in practice, there are unacceptable learning transients. A zero-phase low-pass filter is introduced here to eliminate the worst transients. The main purpose of this paper is to supply a presentation of experiments on a commercial robot that demonstrate the effectiveness of this approach, improving the tracking accuracy of the robot performing a high speed maneuver by a factor of 100 in six repetitions. Experiments using a two-gain ILC reaches this error level in only three iterations. It is suggested that these two simple ILC laws are the equivalent for learning control of proportional and PD control in classical control system design. Thus, what was an impractical approach, becomes practical, easy to apply, and effective.

Design methodology and advances in nested-Miller compensation

Abstract: The nested Miller compensation of three-stage amplifiers is reviewed by using a simple design-oriented approach. The method provides stable amplifiers by accurately controlling the overall phase margin as well as that of the internal loop. Furthermore, the use of nulling resistors to remove the RHP zeros is discussed and optimization criteria are described. A novel technique is presented which allows an amplifier's frequency and settling performance to be greatly improved without increasing power consumption. Thanks to the small compensation capacitors employed, the approach is amenable for integration and in particular where large load capacitors have to be driven. SPICE simulations based on a 0.8-/spl mu/m CMOS design are given and found in remarkable agreement with the theoretical analysis.

Tracking performance limitations in LTI multivariable discrete-time systems

Abstract: In this paper, we investigate tracking properties of linear shift-invariant feedback control systems. We consider the standard unity feedback configuration, and use the energy of an error signal as a measure of tracking ability. Our main goal is to understand the fundamental limitation on tracking performance, which can arise due to the nonminimum phase zeros, unstable poles, and time delays in the plant, and which varies with input reference signals. We consider step, ramp, and sinusoidal signals, and for each type of the signals we derive a closed form expression for the minimum tracking error attainable by any stabilizing controller. Our results display an explicit dependence of the tracking error on nonminimum phase zeros, unstable poles, and in particular the coupling between the directions of the poles and zeros, and those of the input reference signal, upon which a number of useful conclusions can be drawn. One interesting outcome is that not only zero and pole locations affect tracking performance, but their directional properties also play an important role. The paper provides a nontrivial extension of the previously available results to discrete-time systems, with a consideration on broader classes of reference inputs.

Design of 1-D and 2-D variable fractional delay allpass filters using weighted least-squares method

Abstract: In this paper, a weighted least-squares method is presented to design one-dimensional and two-dimensional variable fractional delay allpass filters. First, each coefficient of the variable allpass filter is expressed as the polynomial of the fractional delay parameter. Then, the nonlinear phase error is approximated by a weighted equation error such that the cost function can be converted into a quadratic form. Next, by minimizing the weighted equation error, the optimal polynomial coefficients can be obtained iteratively by solving a set of linear simultaneous equations at each iteration. Finally, the design examples are demonstrated to illustrate the effectiveness of the proposed approach.

Adaptive synchronization design for chaotic systems via a scalar driving signal

Abstract: Using a scalar driving signal, synchronization for a class of chaotic systems has been developed. For chaotic systems characterized by nonlinearity, which depend only on the available output, a unified approach is developed by carefully extending the conventional adaptive observer design. For exactly known chaotic systems, an exponential convergence of synchronization is achieved in the large. When mismatched parameters are presented, this method performs the asymptotic synchronization of output state in the large. The convergence of the estimated parameter error is related to an implicit condition of persistent excitation (PE) on internal signals. From the broad spectrum characteristics of the chaotic driving signal, we reformulate the implicit PE condition as an condition on injection inputs. If this condition is satisfied, the estimated parameters converge to true values and exponential synchronization of all internal states is guaranteed. Two typical examples, including Duffing-Holmes system and Chua's circuit, are considered as illustrations to demonstrate the effectiveness of the adaptive synchronizer. Furthermore, the robustness of adaptive synchronization in the presence of measurement noise is considered where the update law is modified. Finally, numerical simulations and DSP-based experiments show the validity of theoretical derivations.

A note on chaotic secure communication systems

Abstract: This paper presents a new way to transmit and retrieve an information-bearing signal via chaotic systems. In contrast to existing schemes with one transmission line, a two-channel transmission method is adopted for the purpose of faster synchronization and higher security. Basically, an output of the chaotic transmitter is sent for synchronization-only, with no connection to the information signal. The other channel transmits a signal generated from a highly nonlinear function of the chaotic states and the information-bearing signal. While the first channel serves the purpose of efficient synchronization, the second channel is used for complicated encryption and, therefore, improved security/privacy. Simulation results validate the new chaos-based secure communication method.

A modified Volterra series approach for nonlinear dynamic systems modeling

Abstract: This paper describes a modeling approach for nonlinear dynamic systems based on a modified Volterra series; by comparing the truncation error of this series with that of the classical Volterra one, we outlined that, under the assumption of short-term nonlinear memory effects, the modified series enables a single-fold nonlinear convolution integral to be adopted also in the presence of strong nonlinearities. The measurement-based identification of the first terms of the modified Volterra series is described; experimental and simulation results which confirm the theoretical considerations are also provided.

Creation of a complex butterfly attractor using a novel Lorenz-Type system

Abstract: A novel Lorenz-type system of nonlinear differential equations is proposed. Unlike the original Lorenz system, where the chaotic dynamics remain confined to the positive half-space with respect to the Z state variable due to a limiting threshold effect, the proposed system enables bipolar swing of this state variable. In addition, the classical set of parameters (a, b, c) controlling the behavior of the Lorenz system are reduced to a single parameter, namely a. Two possible modes of operation are admitted by the system; switching between these two modes results in the creation of a complex butterfly chaotic attractor. Numerical simulations and results from an experimental setup are presented.

On the jitter requirements of the sampling clock for analog-to-digital converters

Abstract: In this work, the effect of sampling clock jitter on the SNR of an analog-to-digital (AD) conversion is investigated from a practical perspective. Aperture jitter analyses have been dealing up to now with white spectrum jitter. This assumption does not hold for the output of phase-locked loops (PLL)-like frequency synthesizers, where the spectrum is shaped by the loop transfer function. Based on a linear approximation, a powerful expression for the SNR is derived, applicable to a jitter process with a generic autocorrelation function and generic input signal. A lot of different definitions of jitter are available in the literature; this work addresses also the problem of identifying correctly among them the "effective" jitter for a given SNR. This can be profitably used in the specification as well as verification of the jitter requirements of a frequency synthesizer used as sampling clock generator in the AD converter systems. The results have been checked through numerical simulation.

LMIs - a fundamental tool in analysis and controller design for discrete linear repetitive processes

Abstract: Discrete linear repetitive processes are a distinct class of two-dimensional (2-D) linear systems with applications in areas ranging from long-wall coal cutting through to iterative learning control schemes. The feature which makes them distinct from other classes of 2-D linear systems is that information propagation in one of the two distinct directions only occurs over a finite duration. This, in turn, means that a distinct systems theory must be developed for them. In this paper, an LMI approach is used to produce highly significant new results on the stability analysis of these processes and the design of control schemes for them. These results are, in the main, for processes with singular dynamics and for those with so-called dynamic boundary conditions. Unlike other classes of 2-D linear systems, these feedback control laws have a firm physical basis, and the LMI setting is also shown to provide a (potentially) very powerful setting in which to characterize the robustness properties of these processes.

A unified approach for the design of 2-D digital filters via semidefinite programming

Abstract: This paper attempts to demonstrate that a modem optimization methodology known as semidefinite programming (SDP) can serve as the algorithmic core of a unified design tool for a variety of two-dimensional (2-D) digital filters Representative SDP-based designs presented in the paper include minimax and weighted least-squares designs of FIR filters with continuous and discrete coefficients, and minimax design of stable separable-denominator IIR filters Our studies are motivated by the fact that SDP as a subclass of convex programming can be solved efficiently using recently developed interior-point methods and, more importantly, constraints on amplitude/phase responses in certain frequency regions and on stability (for IIR filters), that are often encountered in many filter design problems, can be formulated in a natural way as linear matrix inequalities (LMI) which allow SDP to apply Design examples for each class of filters are included to demonstrate that SDP-based methods can in many cases be useful in producing optimal or near-optimal 2-D filters with reduced computational complexity

Robust D-stability analysis for uncertain discrete singular systems with state delay

Abstract: This work investigates the problem of robust D-stability analysis for uncertain discrete singular systems with state delay and structured uncertainties. Sufficient conditions are developed to ensure that, when the nominal discrete singular delay system is regular, causal and all its finite poles are located within a specified disk, the uncertain system still preserves all these properties when structured uncertainties are added into the nominal system. A computationally simple approach is proposed and a numerical example is given to demonstrate the application of the proposed method.

Controller design and analysis of uncertain piecewise-linear systems

Abstract: This paper presents controller design and analysis methods for uncertain piecewise-linear systems based on a piecewise-smooth Lyapunov function. The basic idea of the proposed approaches is to construct controllers for the uncertain piecewise-linear systems in such a way that a piecewise-continuous Lyapunov function can he used to establish the global stability or the global stability with H/sub /spl infin// performance of the resulting closed loop control systems. It is shown that the control laws can be obtained by solving a set of linear matrix inequalities that are numerically feasible with commercially available software. An example is given to illustrate the application of the proposed methods.

Robust filtering for uncertain linear systems with delayed states and outputs

Abstract: Deals with the robust filtering problem for uncertain linear systems with delayed states and outputs. Both time-invariant and time-varying cases are considered. For the time-invariant case, an algebraic Riccati matrix inequality approach is proposed to design a robust H/sub /spl infin// filter such that the filtering process remains asymptotically stable for all admissible uncertainties, and the transfer function from the disturbance inputs to error state outputs satisfies the prespecified H/sub /spl infin// norm upper bound constraint. We establish the conditions under which the desired robust H/sub /spl infin// filters exist, and derive the explicit expression of these filters. For the time-varying case, we develop a differential Riccati inequality method to design the robust filters. A numerical example is provided to demonstrate the validity of the proposed design approach.

Absolute periodicity and absolute stability of delayed neural networks

Abstract: Proposes to study the absolute periodicity of delayed neural networks. A neural network is said to be absolutely periodic, if for every activation function in some suitable functional set and every input periodic vector function, a unique periodic solution of the network exists and all other solutions of the network converge exponentially to it. Absolute stability of delayed neural networks is also studied in this paper. Simple and checkable conditions for guaranteeing absolute periodicity and absolute stability are derived. Simulations for absolute periodicity are given.

An algorithm for soft-fault diagnosis of linear and nonlinear circuits

Abstract: This brief deals with soft-fault diagnosis of analog circuits. Both ac and dc linear circuits, as well as dc nonlinear circuits with limited number of test points are considered and the presence of component tolerances is taken into account. An approach using the linear-programming concept and the simplex method is developed. Contrary to other methods which use optimization techniques for diagnosis, no optimization process for evaluating the parameter deviations is performed. In fact, only phase 1 of the simplex method is applied to check the existence of a feasible solution. It enables us to state whether the actual parameters are within tolerance ranges or some components are faulty. Identification of the faulty elements is achieved using a similar idea. Three numerical examples illustrate this approach.