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Showing papers in "Asian Journal of Control in 2014"


Journal ArticleDOI
TL;DR: In this article, the robust adaptive controller for the longitudinal dynamics of a generic hypersonic flight vehicle is investigated for the control-oriented model, where the velocity and attitude subsystems are transformed into the linearly parameterized form.
Abstract: In this paper, the robust adaptive controller is investigated for the longitudinal dynamics of a generic hypersonic flight vehicle. The proposed methodology addresses the issue of controller design and stability analysis with respect to parametric model uncertainty and input saturations for the control-oriented model.The velocity and attitude subsystems are transformed into the linearly parameterized form. Based on the parameter projection estimation, the dynamic inverse control is proposed via the back-stepping scheme. In order to avoid the problem of “explosion of complexity,” by introducing a first-order filtering of the synthetic input at each step, the dynamic surface control is designed. The closed-loop system achieves uniform ultimately bounded stability. The compensation design is employed when the input saturations occur. Simulation results show that the proposed approach achieves good tracking performance.

217 citations


Journal ArticleDOI
TL;DR: In this paper, the authors present a first-principles derivation of the LDP for finite state Markov chains, using only simple combinatorial arguments (e.g. the method of types).
Abstract: Large deviation theory is a branch of probability theory that is devoted to a study of the “rate” at which empirical estimates of various quantities converge to their true values. The object of study in this paper is the rate at which estimates of the doublet frequencies of a Markov chain over a finite alphabet converge to their true values. In the case where the Markov process is actually an independent and identically distributed (i.i.d.) process, the rate function turns out to be the relative entropy (or Kullback-Leibler divergence) between the true and the estimated probability vectors. This result is a special case of a very general result known as Sanov's theorem and dates back to 1957. Moreover, since the introduction of the “method of types” by Csiszar and his co-workers during the 1980s, the Proof of this version of Sanov's theorem has been “elementary,” using some combinatorial arguments. However, when the i.i.d. process is replaced by a Markov process, the available Proofs are far more complex. The main objective of this paper is therefore to present a first-principles derivation of the LDP for finite state Markov chains, using only simple combinatorial arguments (e.g. the method of types), thus gathering in one place various arguments and estimates that are scattered over the literature. The approach presented here extends naturally to multi-step Markov chains.

92 citations


Journal ArticleDOI
TL;DR: In this article a Model Predictive Control (MPC) strategy for the trajectory tracking of an unmanned quadrotor helicopter is presented.
Abstract: In this article a Model Predictive Control (MPC) strategy for the trajectory tracking of an unmanned quadrotor helicopter is presented. The quadrotor’s dynamics are modeled by a set of Piecewise Af ...

85 citations


Journal ArticleDOI
TL;DR: In this article, a trajectory tracking problem of a six-degree of freedom (6-DOF) quadrotor unmanned aerial vehicle (UAV) is analyzed and the modified Rodrigues parameters (MRPs) technique is introduced to model the rotational dynamics of the rigid body.
Abstract: This paper deals with the trajectory tracking problem of a six-degree of freedom (6-DOF) quadrotor unmanned aerial vehicle (UAV). The problem of simplified kinematics based on Euler angles is analyzed and the modified Rodrigues parameters (MRPs) technique is introduced to model the rotational dynamics of the rigid body. A nonlinear system error model is established based on the trajectory tracking problem, and, due to the coupling property between the translational and rotational dynamics, we divide the complete closed-loop system into two reduced-order subsystems and a coupling term. The Rodrigues theorem is applied to analyze the internal connections between the coupling term and MRPs. Therefore, the global stability conclusions, by which the trajectory tracking controller of the quadrotor UAV could be designed based on the subsystem directly in future works, are proved based on several assumptions of the subsystems. Thereafter, the controllers, using the backstepping approach and nonlinear disturbance observer/sliding mode control approach, which stabilize the quadrotor UAV globally -exponentially and globally uniformly bounded, are proposed based on the stability theorem proofs mentioned above. Numerical simulations are provided to show that the theoretical conclusions and the controller proposed are effective.

64 citations


Journal ArticleDOI
TL;DR: In this article, a robust fault detection observer for uncertain linear time delay systems is proposed, which is composed of both norm-bounded uncertainties and exogenous signals (noise, disturbance, and fault) which are considered to be unknown.
Abstract: In this paper, a novel approach is proposed to design a robust fault detection observer for uncertain linear time delay systems. The system is composed of both norm-bounded uncertainties and exogenous signals (noise, disturbance, and fault) which are considered to be unknown. The main contribution of this paper is to present unknown input observer (UIO)-based fault detection system which shows the maximum sensitivity to fault signals and the minimum sensitivity to other signals. Since the system contains uncertainty terms, an H∞ model-matching approach is used in design procedure. The reference residual signal generator system is designed so that the fault signal has maximum sensitivity while the exogenous signals have minimum sensitivity on the residual signal. Then, the fault detection system is designed by minimizing the estimation error between the reference residual signal and the UIO residual signal in the sense of H∞ norm. A sufficient condition for the existence of such a filter is exploited in terms of certain linear matrix inequalities (LMIs). Application of the proposed method in a numerical example and an engineering process are simulated to demonstrate the effectiveness of the proposed algorithm. Simulation results show the validity of the proposed approach to detect the occurrence of faults in the presence of modeling errors, disturbances, and noise.

58 citations


Journal ArticleDOI
TL;DR: In this paper, a model reduction problem of positive fractional order systems with a fixed H∞-norm error bound in terms of a linear matrix inequality (LMI) was studied.
Abstract: This paper focuses on the H∞ model reduction problem of positive fractional order systems For a stable positive fractional order system, we aim to construct a positive reduced-order fractional system such that the associated error system is stable with a prescribed H∞ performance Then, based on the bounded real lemma for fractional order systems, a sufficient condition is given to characterize the model reduction problem with a prescribed H∞-norm error bound in terms of a linear matrix inequality (LMI) Furthermore, by introducing a new flexible real matrix variable, the desired reduced-order system matrices are decoupled with the complex matrix variable and further parameterized by the new matrix variable A corresponding iterative LMI algorithm is also proposed Finally, several illustrative examples are given to show the effectiveness of the proposed algorithms

56 citations


Journal ArticleDOI
TL;DR: This paper studies the convergence properties of consensus algorithms for agents with double integrator dynamics communicating over networks modelled by undirected graphs to find that consensus can be achieved, even though the networks along which position and velocity information are shared are different, and not even connected.
Abstract: This paper studies the convergence properties of consensus algorithms for agents with double integrator dynamics communicating over networks modelled by undirected graphs. The positions and velocities of the agents are shared along heterogeneous, i.e. different, undirected communication networks.The main result is that consensus can be achieved, even though the networks along which position and velocity information are shared are different, and not even connected. Insights on the consensus rate are given based only on the topological properties of the network.

51 citations


Journal ArticleDOI
TL;DR: In this paper, an approach of integrated guidance and control (IGC) design for interception of maneuvering targets (evaders) is presented, where an IGC model with uncertainties in the pitch plane is formulated, and, by adopting a backstepping scheme, an adaptive nonlinear IGC approach is developed.
Abstract: This paper presents an approach of integrated guidance and control (IGC) design for interception of maneuvering targets (evaders). An IGC model with uncertainties in the pitch plane is formulated, and, by adopting a backstepping scheme, an adaptive nonlinear IGC approach is developed. Theoretical analysis shows that the design approach makes the line-of-sight (LOS) rate be input-to-state stable (ISS) with respect to target maneuvers and missile model uncertainties, and the stability of the missile dynamics can be guaranteed as well. The numerical simulation confirms the effectiveness of the proposed design approach.

50 citations


Journal ArticleDOI
TL;DR: In this article, the design and operation of a special electromagnetic actuator as a variable engine valve actuator are presented, and a feasible approximated velocity switching estimator based on measurements of current and input voltage to achieve sensorless control.
Abstract: In this paper, the design and operation of a special electromagnetic actuator as a variable engine valve actuator are presented. Further, this paper describes a feasible approximated velocity switching estimator based on measurements of current and input voltage to achieve sensorless control. The proposed concept allows a reduced-order observer to be conceived and yields a specific control strategy with an acceptable performance. In general, this approach represents a viable strategy to build reduced-order observers for estimating the velocity of systems through the measurement of input current and voltage. The robustness of the velocity tracking is explored using a minimum variance approach. The effect of the noise is minimized, and the position can be achieved through an adaptive and optimized structure by combining this particular velocity estimator and an observer based on the electromechanical system. Position control is achieved through an inversion of the model. This approach avoids a more complex structure for the observer and yields an acceptable performance as well as eliminating bulky position-sensor systems. In addition, a control strategy is presented and discussed. Computer simulations of the sensorless control structure are presented in which the positive effects of the observer with optimized parameter setting are visible in the closed-loop control.

44 citations


Journal ArticleDOI
TL;DR: In this paper, an infinite-horizon optimal controller, based on a state-dependent Riccati equation approach, is proposed to solve the tracking problem for nonlinear systems, which results in a state feedback optimal control law plus a time varying term, which minimizes a quadratic performance index.
Abstract: This paper pressents an infinite-horizon optimal controller, based on a state-dependent Riccati equation approach to solve the tracking for nonlinear systems. The synthesized control law comes from solving the Hamilton-Jacobi-Bellman equation for state-dependent coefficient factorized nonlinear systems. The proposed controller results in a state feedback optimal control law plus a time varying term, which minimizes a quadratic performance index. In order to illustrate the tracking to a desired reference, the proposed optimal control law is applied to two systems with practical applications: the Van der Pol oscillator and a doubly fed induction generator. Simulation results illustrate the effectiveness of the control scheme.

40 citations


Journal ArticleDOI
TL;DR: In this article, the robust and accurate trajectory tracking problem for UAVs in the presence of model uncertainties and external disturbances is addressed, where a backstepping controller with disturbance compensation is designed to ensure robust and highly trajectory tracking.
Abstract: This paper addresses the robust and accurate trajectory tracking problem for unmanned helicopters in the presence of model uncertainties and external disturbances. First, the helicopter's model is simplified to a six-degrees-of-freedom rigid body augmented with a simplified rotor dynamic model, with the model uncertainties and the external disturbances being treated as lumped unknown disturbances. Second, a nonlinear disturbance observer is designed to estimate this lumped disturbance. Then, a backstepping controller with disturbance compensation is designed to ensure robust and highly trajectory tracking. After that, the theoretical analysis of the efficiency of the designed disturbance observer-based backstepping controller (Backstepping+DO) is shown by the Lyapunov theory. Finally, simulation results and conclusions are presented and discussed.

Journal ArticleDOI
TL;DR: In this paper, a saturated discontinuous controller is presented by applying the multi-step switching control strategy and the theory of finite-time stability, which can avoid the problem of singularity arising from state or input transformation.
Abstract: In this paper, the saturated practical stabilization problem is addressed for a class of nonholonomic mobile robots based on visual servoing feedback with uncertain camera parameters. The new switching control design method to be proposed is directly based on the original system, which can avoid the problem of singularity arising from state or input transformation. A saturated discontinuous controller is presented by applying the multi-step switching control strategy and the theory of finite-time stability. The closed-loop system can be stabilized to a prescribed arbitrarily small neighborhood of the zero equilibrium point in a finite time. Finally, the simulation results show the effectiveness of the proposed controller design approach.

Journal ArticleDOI
TL;DR: In this article, a robust fractional-order dynamic output feedback sliding mode control (DOF-SMC) technique is introduced for uncertain fractionalorder nonlinear systems, which ensures the asymptotic stability of the fractional order closed-loop system whilst it is guaranteed that the system states hit the switching manifold in finite time.
Abstract: A robust fractional-order dynamic output feedback sliding mode control (DOF-SMC) technique is introduced in this paper for uncertain fractional-order nonlinear systems. The control law consists of two parts: a linear part and a nonlinear part. The former is generated by the fractional-order dynamics of the controller and the latter is related to the switching control component. The proposed DOF-SMC ensures the asymptotical stability of the fractional-order closed-loop system whilst it is guaranteed that the system states hit the switching manifold in finite time. Finally, numerical simulation results are presented to illustrate the effectiveness of the proposed method.

Journal ArticleDOI
TL;DR: In this article, a long baseline (LBL) position and velocity navigation filter for underwater vehicles based directly on the sensor measurements is presented, where the range measurements are explicitly embedded in the filter design, therefore avoiding inversion algorithms and allowing also the consideration of the cases of reduced numbers of readings.
Abstract: This paper presents a novel long baseline (LBL) position and velocity navigation filter for underwater vehicles based directly on the sensor measurements. The solution departs from previous approaches as the range measurements are explicitly embedded in the filter design, therefore avoiding inversion algorithms and allowing also the consideration of the cases of reduced numbers of readings, in particular when there are only two or three distance measurements. The nonlinear system dynamics are considered to their full extent and no linearizations are carried out whatsoever. The filter error dynamics are globally exponentially stable (GES) and it is shown, in a realistic simulation environment, that the filter achieves similar performance to the extended Kalman filter (EKF) and outperforms linear position and velocity filters based on algebraic estimates of the position obtained from the range measurements.

Journal ArticleDOI
TL;DR: In this paper, the synchronization of interconnected k-valued logical networks, as well as that of interconnected higher order K-valued networks, based on their algebraic representations is studied.
Abstract: This paper studies the synchronization of interconnected k-valued logical networks, as well as that of interconnected higher order k-valued logical networks, based on their algebraic representations. For interconnected k-valued logical networks, one necessary and sufficient criterion of synchronization is established via the definition of synchronization and another equivalent condition is given by combining synchronization with fixed points and cycles. Furthermore, with some special properties of semi-tensor product, the third necessary and sufficient condition for synchronization of interconnected k-valued logical networks is raised in terms of transition matrices. Then, the limit set method can be used to analyze the synchronization of interconnected higher order k-valued logical networks. Finally, three examples, including the Boolean model for interconnected biochemical oscillators in the cell cycle, are presented to illustrate effectiveness of the results.

Journal ArticleDOI
TL;DR: This paper establishes a new framework to deal with pseudo‐Boolean inequalities, the optimization problem and the best linear approximation of pseudo‐ Boolean functions, and investigates the optimal control of Boolean control networks, and presents a new optimal control design procedure.

Journal ArticleDOI
TL;DR: In this paper, a new adaptive sliding mode control is proposed to control nonlinear systems with parametric uncertainties and matched and unmatched external disturbances, which is different from the approach of combining the backstepping adaptive scheme and sliding mode controller in the parameter estimation law.
Abstract: In this paper, a new adaptive sliding mode control is proposed to control nonlinear systems with parametric uncertainties and matched and unmatched external disturbances. The proposed method first combines immersion and invariance (I&I) adaptive scheme with sliding mode control (SMC), which preserves the advantages of the two methods. The proposed method is different from the approach of combining the backstepping adaptive scheme and sliding mode control in the parameter estimation law, which allows for prescribed dynamics to be assigned to the estimation error and is easier to tune. Finally, the method is applied to control a class of power systems, and simulation results show the advantages of the proposed method.

Journal ArticleDOI
TL;DR: In this article, the sliding mode control for a class of uncertain switched systems with partial actuator faults is considered and a common integral sliding surface is designed by employing a weighted sum of the input matrices, and the exponential stability of sliding mode dynamics is analyzed by adopting the multiple Lyapunov function method and the average dwell time strategy.
Abstract: This paper considers the sliding mode control for a class of uncertain switched systems with partial actuator faults. By employing a weighted sum of the input matrices, a common integral sliding surface is designed. Moreover, the exponential stability of the sliding mode dynamics is analyzed by adopting the multiple Lyapunov function method and the average dwell time strategy. It is shown that the state trajectory can be driven onto the proposed sliding surface despite the presence of parameter uncertainties, external disturbances, and actuator faults. A numerical example is given to demonstrate the effectiveness of the proposed method.

Journal ArticleDOI
TL;DR: A new image‐based servo control scheme that endows an unmanned aerial vehicle equipped with a robotic arm with the capability of automatically positioning elements on target objects through a new formalism that takes into account the whole system redundancy as well as the peculiarity of under‐actuation related to rotary‐wing crafts.
Abstract: This paper presents a new image-based servo control scheme that endows an unmanned aerial vehicle (UAV) equipped with a robotic arm with the capability of automatically positioning elements on target objects. Through a new formalism, the proposed visual servo scheme controls both the UAV and the manipulator simultaneously. It takes into account the whole system redundancy as well as the peculiarity of under-actuation related to rotary-wing crafts. While it controls the system at the velocity level, it makes use of the mobility afforded by the UAV and the dexterity inherent to robot manipulators. The case of large initial errors is explicitly addressed. Results of simulations are reported to verify the effectiveness of the proposed approach.

Journal ArticleDOI
TL;DR: The results show the NNOMC method owns both better approximating and controlling performance.
Abstract: A neural network on-line modeling and controlling method (NNOMC) is proposed in this paper for multi-variable control of wastewater treatment processes (WWTPs). According to the approximating character of the feedforward neural network (FNN), a modeling FNN is proposed to simulate and decouple WWTPs. Then, an FNN controller for multi-variable control of WWTPs is designed. Moreover, the stability of the NNOMC method is proven in a general inference via the limitation of the learning rate of the FNN. Finally, this proposed NNOMC method is used in the international benchmark of WWTPs. The results show the NNOMC method owns both better approximating and controlling performance.

Journal ArticleDOI
TL;DR: In this article, an on-going work introducing square root extension of cubature-quadrature based Kalman filter is reported, the proposed method is named square-root cubature quadrature kalman filter (SR-CQKF) which propagates and updates square root of the error covariance.
Abstract: In this paper, an on-going work introducing square-root extension of cubature-quadrature based Kalman filter is reported. The proposed method is named square-root cubature-quadrature Kalman filter (SR-CQKF). Unlike ordinary cubature-quadrature Kalman filter (CQKF), the proposed method propagates and updates square-root of the error covariance without performing Cholesky decomposition at each step. Moreover SR-CQKF ensures positive semi-definiteness of the state covariance matrix. With the help of two examples we show the superior performance of SR-CQKF compared to EKF and square root cubature Kalman filter.

Journal ArticleDOI
TL;DR: In this paper, a camera-objective visual kinematic model is introduced by utilizing the pinhole camera model and a unified tracking error system is introduced between the camera and the desired reference trajectory.
Abstract: This paper investigates the finite-time tracking problem of nonholonomic mobile robots in kinematic models via visual servoing in the presence of parametric uncertainties associated with the camera system. First of all, a camera-objective visual kinematic model is introduced by utilizing the pinhole camera model. Second, a unified tracking error system between the camera-objective visual servoing model and the desired reference trajectory is introduced. Third, based on the unified error dynamics and by using the finite-time control method, continuous finite-time controller laws are designed to solve the finite-time tracking problem for the mobile robot in the presence of parametric uncertainties associated with the camera system. Rigorous proof shows that the desired reference trajectory can be tracked in finite time. Finally, an example is employed to verify the efficiency of the proposed methods.

Journal ArticleDOI
TL;DR: In this article, the authors proposed a new method to design observers in a class of nonlinear time-delay systems with delays in system states based on an extension of the well-known state-dependent Riccati equation (SDRE) technique.
Abstract: This paper suggests a new method to design observers in a class of nonlinear time-delay systems with delays in system states. The method is based on an extension of the well-known state-dependent Riccati equation (SDRE) technique. The conditions for locally asymptotic stability of the proposed observer are investigated. Some numerical simulations are provided to show the design procedure and the flexibility of the proposed observer.

Journal ArticleDOI
TL;DR: In this article, the cubature Kalman filtering (CKF) for nonlinear dynamic systems is investigated and a general class of CKFs that use only cubature rules is derived.
Abstract: This paper investigates the cubature Kalman filtering (CKF) for nonlinear dynamic systems This third-degree rule based filter employs a spherical-radial cubature rule to numerically compute the integrals encountered in nonlinear filtering problems, thereby removing the requirements of explicitly computing the Jacobians The cubature rule, however, requires computing the intractable integrals over a high-dimensional spherical region for multidimensional applications Moreover, the cubature formula that has been used to construct the spherical cubature formula has some demerits, most notably its inconvenient properties in computation and low estimation accuracy Aimed at these issues, a general class of CKFs that uses only cubature rules is derived in this paper It can be shown that the conventional CKF is a special case of the proposed algorithm The paper also includes higher-degree CKFs, especially two representative types of the fifth-degree CKFs Performance of the proposed algorithms is demonstrated via two target tracking problems The experimental results, presented herein, illustrate the superior performance of higher-degree CKFs to conventional nonlinear filters

Journal ArticleDOI
TL;DR: In this article, a class of stochastic partial differential equations with Poisson jumps was studied and the existence and uniqueness of the mild solution for the investigated system were established under a reasonable condition, and it was shown that it is pth moment exponentially stable.
Abstract: In this paper, we study a class of stochastic partial differential equations with Poisson jumps, which is more realistic for establishing mathematical models since it has been widely applied in many fields. Under a reasonable condition, we not only establish the existence and uniqueness of the mild solution for the investigated system but also prove that it is pth moment exponentially stable by using the fixed point theory. Then, based on the well-known Borel-Cantelli lemma, further, we prove that the mild solution is almost surely pth moment exponentially stable. Our results improve and generalize those given in the previous literature, in particular, the Lyapunov direct method and successive approximation method. Finally, we give an example to illustrate the effectiveness of the obtained results.

Journal ArticleDOI
TL;DR: In this article, a simple control strategy is proposed to achieve trajectory tracking and fin roll stabilization simultaneously, including surge force, roll moment and yaw moment as control inputs, while position, yaw angle and roll angle are controlled.
Abstract: Trajectory tracking and roll stabilization are both vital practices in ship motion control. Trajectory tracking is a kind of low-frequency control, while roll stabilization by means of fins is a kind of high-frequency control. However, they have been studied separately previously; most tracking control of underactuated surface vessels in the previous studies do not account for roll stabilization by means of fins. In reality, however, they are an integral system. In this paper, a simple control strategy is proposed to achieve trajectory tracking and fin roll stabilization simultaneously. Four degrees of freedom derived from a six degrees of freedom mathematical model of a surface vessel is considered, including surge, sway, roll and yaw. Surge force, roll moment and yaw moment are considered as control inputs, while position, yaw angle and roll angle are controlled. The number of control inputs is fewer than the outputs to be controlled. Therefore, we are dealing with an underactuated problem. An adaptive hierarchical sliding mode control technique is employed to deal with the underactuation. Stabilization of underactuated surface vessels is studied as a special case. Random waves are applied to test the robustness of the designed controllers. Lyapunov stability theory is used to show the stability of closed-loop system. The simulation results verify the effectiveness of the proposed strategy.

Journal ArticleDOI
TL;DR: In this paper, conditions for the existence of robust static output-feedback controllers are established and an iterative convex optimization approach is developed to solve the conditions and the problem of controller synthesis is solved with the help of an analytical formula for the L1-induced norm.
Abstract: This paper is concerned with the design of an L1-induced output-feedback controller for continuous-time positive systems with interval uncertainties. A necessary and sufficient condition for stability and an L1-induced performance of interval positive linear systems is proposed in terms of linear inequalities. Based on this, conditions for the existence of robust static output-feedback controllers are established and an iterative convex optimization approach is developed to solve the conditions. For special single-input-multiple-output (SIMO) positive systems, the problem of controller synthesis is completely solved with the help of an analytical formula for the L1-induced norm. An illustrative example is provided to show the effectiveness and applicability of the theoretical results.

Journal ArticleDOI
TL;DR: In this paper, a neighbor-based flocking protocol was proposed to ensure that all the agents move with a virtual leader's velocity almost surely, and avoidance of collision between the agents is ensured.
Abstract: This paper investigates the flocking problem of multi-agents following a leader with communication delays in a noisy environment. Based on potential fields and the LaSalle-type theorem for stochastic differential delay equations, by introducing the adaptive protocol compensating for the desired velocity, a new neighbor-based flocking protocol is proposed such that all the agents move with a virtual leader's velocity almost surely, and avoidance of collision between the agents is ensured. A numerical example is given to illustrate the effectiveness of the proposed methods.

Journal ArticleDOI
TL;DR: The result shows how the bandwidth and networked induced‐delay of a communication channel may fundamentally constrain a control system's tracking capability.
Abstract: The best tracking problem for a single-input-single-output (SISO) networked control system with communication constraints is studied in this paper. The tracking performance is measured by the energy of the error signal between the output of the plant and the reference signal. The communication constraints under consideration are finite bandwidth and networked induced-delay. Explicit expressions of the minimal tracking error have been obtained for networked control systems with or without communication constraints. It is shown that the best tracking performance dependents on the nonminimum phase zeros, and unstable poles of the given plant, as well as the bandwidth and networked induced-delay. It is also shown that, if the constraints of the communication channel do not exist, the best tracking performance reduces to the existing tracking performance of the control system without communication constraints. The result shows how the bandwidth and networked induced-delay of a communication channel may fundamentally constrain a control system's tracking capability. Some typical examples are given to illustrate the theoretical results.

Journal ArticleDOI
TL;DR: An interval type‐2 (IT2) fuzzy static output feedback controller is designed to stabilize the IT2 Takagi‐Sugeno (T‐S) fuzzy system to reduce the conservativeness of stability analysis.
Abstract: This study aims to design an interval type-2 (IT2) fuzzy static output feedback controller to stabilize the IT2 Takagi-Sugeno (T-S) fuzzy system. Conservative results may be obtained when a common quadratic Lyapunov function is utilized to investigate the stability of T-S fuzzy systems. A fuzzy Lyapunov function is employed in this study to analyze the stability of the IT2 fuzzy closed-loop system formed by the IT2 T-S fuzzy model and the IT2 fuzzy static output feedback controller. Stability conditions in the form of linear matrix inequalities are derived. Several slack matrices are introduced to further reduce the conservativeness of stability analysis. The membership-function shape-dependent analysis approach is also employed to relax the stability results. The numerical examples illustrate the effectiveness of the proposed conditions.