Shaosheng Zhou

H∞ filtering of discrete-time fuzzy systems via basis-dependent Lyapunov function approach

This paper is concerned with the H~ filtering problem for a class of discrete-time fuzzy systems. Attention is focused on the design of a stable filter guaranteeing a prescribed noise attenuation level in the H~ sense. By using basis-dependent Lyapunov functions, sufficient conditions for the solvability of this problem are obtained. It has been shown that the H~ filtering problem can be solved as a linear matrix inequality (LMI) optimization problem. Two examples are provided to demonstrate the applicability of the proposed approach.

Control Design for Fuzzy Systems Based on Relaxed Nonquadratic Stability and

In this paper, new approaches to Hinfin controller design for a class of discrete-time nonlinear fuzzy systems are proposed based on a relaxed approach in which basis-dependent Lyapunov functions are used. First, two relaxed conditions of nonquadratic stability with H infin norm bound are presented for this class of systems. The two relaxed conditions are shown to be useful in designing fuzzy control systems. By introducing some additional instrumental matrix variables, the two relaxed conditions are used to develop Hinfin controllers. In the control design, the first relaxed condition has fewer inequality constraints, but only admits a common additional matrix variable while the second one can admit multiple additional matrix variables. Finally, two examples are given to demonstrate the applicability of the proposed approach

H_{\infty}

This article deals with an output feedback H ∞ control problem for a class of discrete-time fuzzy dynamic systems. A full-order dynamic output feedback H ∞ control design approach is developed by combining a fuzzy-basis-dependent Lyapunov function and a transformation on the controller parameters, which leads to sufficient conditions in the form of strict linear matrix inequalities (LMIs). The fuzzy-basis-dependent results are less conservative due to the generality of the fuzzy-basis-dependent Lyapunov function used which includes the fuzzy-basis-independent one as a special case. It has been shown that the underling full-order dynamic output feedback H ∞ control problem can be solved as LMI optimization problems that can be computed numerically very efficiently. Finally, two numerical examples, concerning the control of a discrete-time chaotic Lorenz system and an inverted pendulum, are given to demonstrate the applicability of the proposed approach.

Performance Conditions

This paper investigates the problem of stability analysis and stabilization for two-dimensional (2-D) discrete fuzzy systems. The 2-D fuzzy system model is established based on the Fornasini–Marchesini local state-space model, and a control design procedure is proposed based on a relaxed approach in which basis-dependent Lyapunov functions are used. First, nonquadratic stability conditions are derived by means of linear matrix inequality (LMI) technique. Then, by introducing an additional instrumental matrix variable, the stabilization problem for 2-D fuzzy systems is addressed, with LMI conditions obtained for the existence of stabilizing controllers. Finally, the effectiveness and advantages of the proposed design methods based on basis-dependent Lyapunov functions are shown via two examples.

Dynamic output feedback H∞ control of discrete-time fuzzy systems: a fuzzy-basis-dependent Lyapunov function approach

This article considers the delay-dependent H ∞ control problem for linear neutral systems with both discrete and distributed delays. The problem we address is to design a state feedback controller such that the resulting closed-loop system is asymptotically stable and satisfies a prescribed H ∞ performance level. First, a delay-dependent sufficient condition for the solvability of the problem is obtained in terms of matrix inequalities. Then, by using the cone complementarity linearization approach, an H ∞ controller is developed based on the solvability condition. Finally, numerical examples are provided to demonstrate the effectiveness of the proposed method.

Stability analysis and control design for 2-D fuzzy systems via basis-dependent Lyapunov functions

ABSTRACT This paper addresses two kinds of dual approaches to stability and stabilisation of uncertain switched positive systems under arbitrary switching and average dwell-time switching, respectively. The uncertainties in systems refer to polytopic ones. A new parameter-dependent switched linear copositive Lyapunov function is first proposed for uncertain switched positive systems. By using the new Lyapunov function associated with arbitrary switching and average dwell-time switching, respectively, sufficient conditions for the stability of the systems are established. Two alternative stability criteria based on two kinds of dual approaches are addressed. It is shown that the alternative criteria hold for not only the primal switched positive system but also its dual system. Then, the stabilisation of primal and dual switched positive systems under arbitrary switching and average dwell-time switching is solved, respectively. All present conditions are solvable in terms of linear programming. By some comparisons with existing results, the less conservativeness of the obtained results is verified. Finally, a practical example is provided to illustrate the effectiveness of the theoretical findings.