Narrow Results

This paper investigates the problem of finite-time $H_{\infty }$ synchronization for semi-Markov jump Lur’e systems with time-varying delay and external disturbance. The purpose of this work is to design a mode-dependent state-feedback controller to ensure that the synchronization-error system achieves finite-time synchronization with a prescribed $H_{\infty }$ performance index. A criterion for the finite-time synchronization is proposed by using appropriate Lyapunov functional and two recently developed inequalities. Then, a design method for the required state-feedback controller is presented with the application of several decoupling techniques. Finally, an example is provided to illustrate the applicability of the proposed control method.

This paper is dedicated to investigating the asymptotic synchronization of delayed Lur’e systems via non-fragile aperiodic sampled-data control. Two different kinds of gain fluctuations are taken into consideration. A time-dependent two-sided looped functional is proposed, which makes efficient use of the obtainable information not only of the whole sampling intervals, but also of the nonlinear functions of the considered systems. A criterion on global asymptotic stability is derived by means of the constructed looped functional and using the free-weighting matrix approach. Then, a non-fragile aperiodic sampled-data controller, which allows both additive and multiplicative gain fluctuations, is designed to ensure the asymptotic synchronization based on solutions of a set of linear matrix inequities. Finally, an example with simulations is presented, which shows that the designed controller allows a larger sampling period in comparison with the existing results.

This paper studies a master-slave type of chaos synchronization problem for a general form of Lur'e systems by a time-delay feedback control technique, improving some results of Yalçin et al. [2001]. Some fairly simple algebraic conditions are derived for easier verification, facilitating the design and applications of such chaos synchronization systems.

In this paper, we propose a method to research lag synchronization of the identical master-slave chaotic Lur'e systems via replacing variables control with time delay. By means of absolute stability theory, we prove two types of sufficient conditions for the lag synchronization: Lur'e criterion and frequency domain criterion. Based on the criteria, we suggest an optimization scheme to design the control variables. Applying the scheme to general Chua's circuits, we obtain the parameter ranges in which the master-slave Chua's circuits laggingly synchronize or not by varied single-variable control. Finally, we cite the examples by illustration of the results.

Some frequency domain criteria for chaos synchronization of Lur'e system by linear state error feedback control are proposed and applied to design the controller that synchronizes the master-slave Chua's circuits coupled by linear state error feedback. A simple synchronization controller is obtained.

In this paper, an observer-based adaptive feedback controller is developed for a class of chaotic systems. This controller does not need the availability of state variables. It can be used for tracking a smooth orbit that can be a limit cycle or a chaotic orbit of another system. This adaptive feedback controller is constructed with the aid of its H^∞ control technique to achieve the H^∞ tracking performance. Based on Lyapunov stability theorem, the proposed adaptive feedback control system can guarantee the stability of whole closed-loop system and obtain good tracking performance as well. To demonstrate the efficiency of the proposed scheme, two well-known chaotic systems, namely Chua's circuit and Lur'e system are considered as illustrative examples.

The sufficient conditions for chaos synchronization of two nonidentical systems by replacing variables control have not been proposed until now. In this paper, synchronization of two chaotic Lur'e systems with parameter mismatch by replacing variables control is studied. First of all, we present a master-slave Lur'e systems synchronization scheme with both parameter mismatch and replacing variables control, and derive a responsive error system for the scheme. A new definition of synchronization with finite L₂-gain is then introduced. Based on the definition, the sufficient synchronization criteria which are in the form of linear matrix inequality (LMI) are proved using a quadratic Lyapunov function. By means of MKY lemma the frequency domain criteria are further derived from the obtained LMIs. These frequency domain criteria are illustrated on the master-slave Chua's circuits with parameter mismatch so that the ranges of the parameters of Chua's circuit are analytically solved in the sense of the synchronization with finite L₂-gain by replacing singe-variable control. The illustrative examples verify that within the ranges of the parameters it is possible to synchronize the master-slave Chua's circuits up to a small synchronization error bound, even the qualitative behaviors of the slave circuit are different from that of the master one, such as the trajectory of the master circuit is chaotic and that of the slave divergent. The relation between the synchronization error bound and parameter mismatch is shown.

In this paper, a new approach to analyze the asymptotic, exponential and robust stability of the master-slave synchronization for Lur'e systems using time-varying delay feedback control is proposed. The discussion is motivated by the problem of transmitting information in optical communication systems using chaotic lasers. The approach is based on the Lyapunov–Krasovskii stability theory for functional differential equations and the linear matrix inequality (LMI) technique with the use of a recent Leibniz–Newton model based transformation, without including any additional dynamics. Using the problem of synchronizing coupled Chua's circuits, three examples are given to illustrate the effectiveness of the proposed methodology.

This paper deals with the problems of stability analysis and control synthesis with performance for the master-slave synchronization of Lur'e systems using a time-delay feedback control. The proposed approach consists in obtaining a new improved robust stability criteria as well as a control law based on linear matrix inequalities (LMIs) via discretized Lyapunov–Krasovskii functional combined with an alternative strategy based on the introduction of slack variables to allow the decoupling of the system matrices from the Lyapunov matrices. Using the problem of synchronizing coupled Chua's circuits, two examples are presented to illustrate the effectiveness of the proposed methodology.

The problem of control synthesis for master–slave synchronization of continuous time chaotic systems of Lur'e type using sampled feedback control subject to sampling time random fluctuation and data packet dropouts is investigated. New stability and stabilization conditions are proposed based on Linear Matrix Inequalities (LMIs). The idea is to connect two very efficient approaches to deal with delayed systems: the discretized Lyapunov functional for systems with pointwise delay and the convex analysis for systems with time-varying delay. Simulation examples based on synchronizing coupled Chua's circuits are used to illustrate the effectiveness of the proposed methodology.

This paper investigates the global lagged finite-time synchronization of the master-slave Lur’e systems subject to time delay of signal transmission. By designing a variable-substitution and feedback controller, a master-slave finite-time synchronization scheme for the Lur’e systems with time delay is built up. Two delay-independent global lagged finite-time synchronization criteria are proved in the forms of linear matrix inequalities (LMIs), and the corresponding settling time of synchronization is analytically estimated. The obtained LMI criteria are applied to Chua’s oscillators, obtaining some easily implemented algebraic criteria under various single-variable-substitution and feedback controller, which are then optimized to improve their conservative property. Finally, several numerical examples are illustrated to verify the effectiveness of the optimized criteria.