Stability and H/sub ∞/ disturbance attenuation analysis for symmetric Takagi-Sugeno fuzzy systems

Abstract

We study the stability and H/sub /spl infin// disturbance attenuation properties for a class of Takagi-Sugeno fuzzy systems composed of a finite number of linear time-invariant symmetric subsystems. We focus our attention on discrete-time systems. We show that when all the subsystems are Schur stable, the fuzzy system is asymptotically stable under arbitrary IF-THEN rule. Furthermore, we show that when all the subsystems are Schur stable and have the H/sub /spl infin// disturbance attenuation level less than a constant /spl gamma/, the fuzzy system is asymptotically stable and achieves the H/sub /spl infin// disturbance attenuation level /spl gamma/ under arbitrary IF-THEN rule. The key idea for both stability and H/sub /spl infin// disturbance attenuation analysis In this work is to establish a common Lyapunov function for all the subsystems in the fuzzy system.