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This paper is concerned with theH∞filtering problem for a class of continuous-time linear switched systems with the asynchronous behaviours, where ‘asynchronous’ means that the switching of the filters to be designed has a lag to the switching of the system modes. By using the Lyapunov-like functions and the average dwell time technique, a sufficient condition is obtained to guarantee the asymptotic stability with a weightedH∞performance index for the filtering error system. Moreover, the results are formulated in the form of linear matrix inequalities that are numerical feasible. As a result, the filter design problem is solved. Finally, an illustrative numerical example is presented to show the effectiveness of the results. [ABSTRACT FROM AUTHOR]

This paper is concerned with the stability and L2-gain problems for a class of continuous-time linear switched systems with the existed asynchronous behaviors, where 'asynchronous' means that the switching of the controllers to be designed has a lag to the switching of the system modes. Firstly, a new sufficient condition on the asymptotic stability and weighted L2-gain analysis is obtained by using multiple Lyapunov functions combined with the average dwell time technique. Moreover, a result that is formulated in form of linear matrix inequalities is derived for the problem of asynchronous H ∞ control. Based on the result, the mode-dependent controllers can be designed. Finally, an illustrative numerical example is presented to show the effectiveness of the obtained results.Copyright © 2013 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this study, the authors mainly deal with the asynchronous stabilisation problem for a class of continuous‐time impulsive switched systems. By using multiple Lyapunov functions combined with mode‐dependent average dwell time, the exponential stability sufficient condition of closed‐loop systems is derived. Based on the stability result, the problem of asynchronous stabilisation is solved under a proper control law. Moreover, the stability and stabilisation results are formulated in the form of linear matrix inequalities that are numerical feasible. Finally, an illustrative numerical example is presented to show the effectiveness of the obtained results. [ABSTRACT FROM AUTHOR]

This paper investigates the delay-dependent stability of continuous-time fuzzy interconnected systems with time-varying delays. The fuzzy interconnected system consists ofinterconnected continuous-time Takagi–Sugeno fuzzy subsystems. A stability criterion based on fuzzy Lyapunov–Krasovskii functional is proposed to guarantee the asymptotic stability of fuzzy time-delay interconnected systems. In the derivation process, some free fuzzy weighting matrices are introduced among the terms of the system equation to yield less conservative results. The proposed stability criterion can be obtained by solving a set of linear matrix inequalities that are numerically feasible. Finally, two numerical examples are provided to demonstrate the effectiveness of the present method. [ABSTRACT FROM AUTHOR]

This paper deals with the stability of nonlinear discrete-time positive systems with time-varying delays represented by the Takagi-Sugeno (T-S) fuzzy model. The time-varying delays in the systems can be unbounded. Sufficient conditions of stability which are not relevant to the magnitude of delays are derived by a solution trajectory. Based on the stability results, the problems of controller design via the parallel distributed compensation (PDC) scheme are solved. The control is under the positivity constraint, which means that the resulting closed-loop systems are not only stable, but also positive. Constrained control is also considered, further requiring that the state trajectory of the closed-loop system be bounded by a prescribed boundary if the initial condition is bounded by the same boundary. The stability results and control laws are formulated as linear matrix inequalities (LMIs) and linear programs (LPs). A numerical example and a real plant are studied to demonstrate the application of the proposed methods. [ABSTRACT FROM AUTHOR]

This study focuses on the problem of delay‐dependent H∞ filter design for non‐linear interconnected systems with time‐varying delays via Takagi–Sugeno fuzzy models. Based on the delay‐dependent fuzzy Lyapunov–Krasovskii functional and the fuzzy‐free weighting matrix technique, the delay‐dependent stability and a prescribed H∞ performance index are guaranteed for the overall filtering‐error system. In addition, a sufficient condition for the existence of such a filter is established by using linear matrix inequalities that are numerically feasible. Finally, two examples are given to demonstrate the effectiveness and advantage of the proposed approach. [ABSTRACT FROM AUTHOR]

This paper deals with the stability of nonlinear continuous-time positive systems with delays represented by the Takagi-Sugeno (T-S) fuzzy model. A simpler sufficient condition of stability based on linear copositive Lyapunov functional (LCLF) is derived which is not relevant to the magnitude of delays. Based on the result of stability, the problem of controller design via the so-called parallel distributed compensation (PDC) scheme is solved. The control is under a positivity constraint, which means that the resulting closed-loop systems are not only stable, but also positive. Constrained positive control is also considered, further requiring that the trajectory of the closed-loop system is bounded by a prescribed boundary if the initial condition is bounded by the same boundary. The stability results are formulated as linear programs (LPs) and linear matrix inequalities (LMIs), and the control laws can be obtained by solving a set of bilinear matrix inequalities (BMIs). A numerical example and a real plant are studied to demonstrate the efficiency of the proposed method. [ABSTRACT FROM AUTHOR]

This article considers the decentralised H ∞ filtering of interconnected discrete-time fuzzy systems with time delays based on piecewise Lyapunov–Krasovskii functionals. The fuzzy system consists of J interconnected time-delay discrete-time Takagi–Sugeno fuzzy subsystems and the decentralised H ∞ filter is designed for each subsystem. It is shown that the stability with H ∞ performance of overall filtering error system can be established if a piecewise Lyapunov–Kroasovskii functional can be constructed, and moreover, the functional can be obtained by solving a set of linear matrix inequalities that are numerically feasible. A simulation example is given to show the effectiveness of the presented approach. [ABSTRACT FROM AUTHOR]

This paper studies the problems of the stochastic stabilization and H control of a class of nonlinear stochastic systems that can be represented by a stochastic heterogeneous model. Based on this model, the problem of stabilization with state feedback controller is first considered, and a new H controller design method is then developed. Synthesis of both stabilization and H controller is based on the solutions of linear matrix inequalities (LMIs). Finally, an example is given to illustrate the effectiveness of the approach proposed in this paper. [ABSTRACT FROM AUTHOR]