A New Design of Membership-Function-Dependent Controller for T-S Fuzzy Systems Under Imperfect Premise Matching

This paper examines the problem of membership-function-dependent controller design for a class of discrete-time T-S fuzzy systems. Based on the partition method of premise variable space, the original T-S fuzzy model is equivalently converted into a piecewise-fuzzy system. Then, by employing some staircase functions, the continuous membership functions are approximated by a series of discrete values via which the information of membership functions is brought into the stability analysis to reduce the design conservatism. With piecewise-Lyapunov functions, the approaches to the piecewise-fuzzy state feedback and observer-based output feedback controller design are proposed, respectively, in terms of linear matrix inequalities such that the closed-loop system is asymptotically stable with a prescribed H_∞ performance level. It is shown that the membership functions of the fuzzy model and fuzzy controllers are not necessarily the same, which allows more design flexibility. Finally, two illustrative examples are provided to show the effectiveness of the developed methods.

I. Introduction

It is known that nearly all the physical plants and industrial processes in practice are nonlinear, and these different kinds of nonlinearities impose great difficulties on stability analysis and controller synthesis. During the past few decades, as an effective way to tackle these complex nonlinear systems, fuzzy logic control has received much attention in control community. The fuzzy logic control provides a means of converting a linguistic control strategy based on expert knowledge into an automatic control strategy, and many significant results reported in the literature have shown that it offers an effective method for the control problem of complex nonlinear systems or even nonanalytic systems (refer to [1]–[7] and references therein). To mention a few, in [5] a fuzzy logic controller was designed and implemented on a test vehicle for the lateral motion control, which is modularized as a feedback, preview, and gain scheduling rule bases. The results on stability analysis of continuous-time fuzzy-model-based control systems were reviewed in [2], where some fundamental and essential aspects related to membership-function-dependent analysis methods are summarized. In [6], the problem of robust adaptive fuzzy cooperative tracking control for a class of uncertain nonlinear multiagent systems was studied, which are subject to time delays and dead-zone nonlinearities. For a class of chaotic systems with unknown functions and disturbances, the problem of asymptotic stabilization for such systems were investigated in [7] based on the adaptive fuzzy logic control theory.