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

We study the stability and H_∞ 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_∞ disturbance attenuation level less than a constant γ, the fuzzy system is asymptotically stable and achieves the H_∞ disturbance attenuation level γ under arbitrary IF-THEN rule. The key idea for both stability and H_∞ disturbance attenuation analysis In this work is to establish a common Lyapunov function for all the subsystems in the fuzzy system.