Feedback Control of T-S Fuzzy Systems Based on LTV System Theory

Abstract

Takage-Sugeno (T-S) fuzzy systems are equivalent to linear time-varying (LTV) systems; the theory of LTV systems can therefore be used to design global feedback controllers to stabilise T-S fuzzy systems. In this paper, a T-S fuzzy system is first transformed into its canonical form in terms of a Lyapunov transform. A global feedback controller can then be designed to assign all parallel D-spectrum eigenvalues (PD eigenvalues) of the closed-loop T-S fuzzy system to the desired locations with negative extended means. The advantage of the proposed scheme is that it allows us to design a single feedback controller to regulate the closed-loop T-S fuzzy system in the whole state-space, and guarantee that the closed-loop system is globally asymptotically stable. A simulation example is given in support of the proposed scheme.