H_∞ Synchronization of Chaotic Systems via Delayed Feedback Control

The H∞ synchronization problem for a class of delayed chaotic systems with external disturbance is investigated. A novel delayed feedback controller is established under which the chaotic master and slave systems are synchronized with a guaranteed H∞ performance. Based on the Lyapunov stability theory, a delay-dependent condition is derived and formulated in the form of linear matrix inequality (LMI). A numerical simulation is also presented to validate the effectiveness of the developed theoretical results...     

H∞ Synchronization of Chaotic Systems via Delayed Feedback Control

The H∞ synchronization problem for a class of delayed chaotic systems with external disturbance is investigated. A novel delayed feedback controller is established under which the chaotic master and slave systems are synchronized with a guaranteed H∞ performance. Based on the Lyapunov stability theory, a delay-dependent condition is derived and formulated in the form of linear matrix inequality (LMI). A numerical simulation is also presented to validate the effectiveness of the developed theoretical results.     

H_∞ controller synthesis of piecewise discrete time linear systems

This paper presents an H∞ controller design method for piecewise discrete time linear systems based on a piecewise quadratic Lyapunov function. It is shown that the resulting closed loop system is globally stable with guaranteed H∞ performance and the controller can be obtained by solving a set of bilinear matrix inequalities. It has been shown that piecewise quadratic Lyapunov functions are less conservative than the global quadratic Lyapunov functions. A simulation example is also given to illustrate the advantage of the proposed approach.     

Delay-dependent robust stabilization and H ∞ control for uncertain stochastic T-S fuzzy systems with discrete interval and distributed time-varying delays

In this paper, delay-dependent robust stabilization and H∞ control for uncertain stochastic Takagi-Sugeno (T-S) fuzzy systems with discrete interval and distributed time-varying delays are discussed. The purpose of the robust stochastic stabilization problem is to design a memoryless state feedback controller such that the closed-loop system is mean-square asymptotically stable for all admissible uncertainties. In the robust H∞ control problem, in addition to the mean-square asymptotic stability requirement, a prescribed H∞ performance is required to be achieved. Sufficient conditions for the solvability of these problems are proposed in terms of a set of linear matrix inequalities (LMIs) and solving these LMIs, a desired controller can be obtained. Finally, two numerical examples are given to illustrate the effectiveness and less conservativeness of our results over the existing ones.     

Robust stability and stabilization of discrete singular systems with interval time-varying delay and linear fractional uncertainty

The robust stability and robust stabilization problems for discrete singular systems with interval time-varying delay and linear fractional uncertainty are discussed. A new delay-dependent criterion is established for the nominal discrete singular delay systems to be regular, causal and stable by employing the linear matrix inequality (LMI) approach. It is shown that the newly proposed criterion can provide less conservative results than some existing ones. Then, with this criterion, the problems of robust stability and robust stabilization for uncertain discrete singular delay systems are solved, and the delay-dependent LMI conditions are obtained. Finally, numerical examples are given to illustrate the e?ectiveness of the proposed approach.     

H_∞ Control for 2-D Discrete State Delayed Systems in the Second FM Model

This paper is concerned with the problem of H_∞control for two-dimensional (2-D) discrete state delay systems described by the second Fornasini and Marchesini (FM) state- space model.A sufficient condition to have an H_∞noise atten- uation for this 2-D system is given in terms of a certain linear matrix inequality (LMI).The optimal H_∞controller is obtained by solving a convex optimization problem.Finally,a simulation example is given to illustrate the effectiveness of the proposed result.     

H2 /H∞ control of networked control system with random time delays

This paper investigates the H 2 /H ∞ control problem for a class of discrete-time networked control systems with random communication time delays. Both sensor-to-controller (S-C) and controller-to-actuator (C-A) random network-induced delays are considered. Two independent Markov chains are used to model the S-C and C-A random delays. The resulting closed-loop system is a jump linear time-delay system induced by two Markov chains. Sufficient conditions for existence of H 2 /H ∞ controller are established by free-weighting matrix and stochastic Lyapunov functions. A simulation example illustrates the effectiveness of the proposed method.     

Gain-scheduled L-one control for linear parameter-varying systems with parameter-dependent delays

This paper deals with the problem of gain-scheduled L-one control for linear parameter-varying (LPV) systems with parameter-dependent delays. The attention is focused on the design of a gain-scheduled L-one controller that guarantees being an asymptotically stable closed-loop system and satisfying peak-to-peak performance constraints for LPV systems with respect to all amplitude-bounded input signals. In particular, concentrating on the delay-dependent case, we utilize parameter-dependent Lyapunov functions (PDLF) to establish peak-to-peak performance criteria for the first time where there exists a coupling between a Lyapunov function matrix and system matrices. By introducing a slack matrix, the decoupling for the parameter-dependent time-delay LPV system is realized. In this way, the sufficient conditions for the existence of a gain-scheduled L-one controller are proposed in terms of the Lyapunov stability theory and the linear matrix inequality (LMI) method. Based on approximate basis function and the gridding technique, the corresponding controller design is cast into a feasible solution problem of the finite parameter linear matrix inequalities. A numerical example is given to show the effectiveness of the proposed approach.     

一类不确定Lur'e奇异系统的可靠鲁棒H_∞跟踪控制(英文)

The problem of reliable robust H_∞tracking control for a class of uncertain Lur'e singular systems is studied.A practical and general failure model of actuator and sensor is considered by using convex polytopic uncertainties to describe control surface impairment.Some sufficient conditions are presented for the case of actuator,sensor and control surface failures in terms of linear matrix inequalities (LMIs).The resultant control systems are reliable in that they guarantee closed-loop system robust stability with H_∞performance and the output tracking the reference signal without steady-state error when all control components are operational as well as when some control components experience failures.Finally,a numerical example is given to show the effectiveness of the proposed methods.     

Enhanced H∞ Filtering for Continuous-time State-delayed Systems

The H∞ filtering problem for continuous-time polytopic uncertain time-delay systems is investigated. Attention is focused on the design of full-order filters guaranteeing a prescribed H∞ attenuation level for the filtering error system. First, a simple alternative proof is given for an improved linear matrix inequality （LMI） representation of H∞ performance. Then, based on the performance criterion which keeps Lyapunov matrices out of the product of system dynamic matrices, a suficient condition for the existence of robust estimators is formulated in terms of LMIs, and the corresponding filter design is cast into a convex optimization problem which can be effciently handled by using standard numerical algorithms. It is shown that the proposed design strategy allows the use of parameter-dependent Lyapunov functions and hence it is less conservative than some earlier results. A numerical example is employed to demonstrate the feasibility and advantage of the proposed design.     

Fault detection for a class of impulsive switched systems

The problem of fault detection for a class of nonlinear impulsive switched systems is investigated in this paper. Fault detection filters are designed such that the augmented systems are stable, and the residual error signal generated by the filters guarantees the H∞ performance for disturbances and faults. Sufficient conditions for the design of fault detection(FD) filters are presented by linear matrix inequalities. Moreover, the filter gains are characterized according to a solution of a convex optimization. Finally, an example derived from a pulse-width-modulation-driven boost converter is given to illustrate the effectiveness of the FD design approach.     

Peak-to-Peak Gain Minimization for Uncertain Linear Discrete Systems： A Matrix Inequality Approach

A matrix inequality approach to peak-to-peak gain minimization for a class of uncertain linear discrete systems is studied. We minimize the ＊-norm, which is the best upper bound on the induced L∞ norm obtained by bounding the reachable set with inescapable ellipsoids, instead of minimizing the induced L∞ norm directly. Based on this idea, the problems of robust peak-to-peak gain minimization and controller synthesis are reduced to solving the feasibility problems of a set of matrix inequalities. A numerical example is used to demonstrate the feasibility and effectiveness of the presented method.     

具有非线性扰动和混合时滞的中立型系统的时滞依赖鲁棒稳定性

This paper concerns the delay-dependent robust stability problem of uncertain neutral systems with mixed neutral and discrete delays. Nonlinear time-varying parameter perturbations are considered. Based on the newly established integral inequalities, the neutral-delay-dependent and discrete-delay-dependent stability criterion is derived without using a fixed model transformation. The condition is presented in terms of linear matrix inequality and can be easily solved by existing convex optimization techniques. A numerical example is given to demonstrate the less conservatism of the proposed results.     

Stability analysis for discrete linear systems with state saturation by a saturation-dependent Lyapunov functional

This paper concerns the stability analysis problem of discrete linear systems with state saturation using a saturation-dependent Lyapunov functional.We introduce a free matrix characterized by the sum of the absolute value of each elements for each row less than 1,which makes the state with saturation constraint reside in a convex polyhedron.A saturation-dependent Lyapunov functional is then designed to obtain a sufficient condition for such systems to be globally asymptotically stable.Based on this stability criterion,the state feedback control law synthesis problem is also studied.The obtained results are formulated in terms of bilinear matrix inequalities that can be solved by the presented iterative linear matrix inequality algorithm.Two numerical examples are used to demonstrate the effectiveness of the proposed method.     

Output Feedback Tracking Control for a Class of Switched Nonlinear Systems with Time-varying Delay

This paper studies the problem of tracking control for a class of switched nonlinear systems with time-varying delay. Based on the average dwell-time and piecewise Lyapunov functional methods, a new exponential stability criterion is obtained for the switched nonlinear systems. The designed output feedback H∞controller can be obtained by solving a set of linear matrix inequalities(LMIs).Moreover, the proposed method does not need that a common Lyapunov function exists for the switched systems, and the switching signal just depends on time. A simulation example is provided to demonstrate the effectiveness of the proposed design scheme.     

具有测量数据部分丢失的离散系统的H∞滤波器设计

For packet-based transmission of data over a network, or temporary sensor failure, etc., data samples may be missing in the measured signals. This paper deals with the problem of H∞ filter design for linear discrete-time systems with missing measurements. The missing measurements will happen at any sample time, and the probability of the occurrence of missing data is assumed to be known. The main purpose is to obtain both full-and reduced-order filters such that the filter error systems are exponentially mean-square stable and guarantee a prescribed H∞ performance in terms of linear matrix inequality (LMI). A numerical example is provided to demonstrate the validity of the proposed design approach.     

Modeling and control for wireless networked control system

In this paper, the stabilization problem is considered for the class of wireless networked control systems (WNCS). An indicator is introduced in the WNCS model. The packet drop sequences in the indicator are represented as states of a Markov chain. A new discrete Markov switching system model integrating 802.11 protocol and new scheduling approach for wireless networks with control systems are constructed. The variable controller can be obtained easily by solving the linear matrix inequality (LMI) with the use of the Matlab toolbox. Both the known and unknown dropout probabilities are considered. Finally, a simulation is given to show the feasibility of the proposed method.