Stabilization of T-S fuzzy systems using LTV system theory

Takagi-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 stabilize T-S fuzzy systems. It is seen that the closed-loop T-S fuzzy system is first transformed into the canonical form by using a Lyapunov transform, a global feedback controller is then designed to assign all Parallel D-spectrum eigenvalues (PD-eigenvalues) of the closed-loop T-S fuzzy system to the desired locations whose real parts have negative extended means. The proposed control scheme not only guarantees asymptotic stability of the closed-loop T-S fuzzy systems, but also allows the designers to directly design a simple global controller instead of deriving a complex global controller by aggregating all local controllers using fuzzy membership functions. A simulation example is given in support of the proposed scheme.