Stability of T-S model based fuzzy control systems — Virtual equivalent system approach

This paper is concerned with the stability of T-S model based fuzzy control systems for continuous, linear time-invariant plant. In contrast to the Lyapunov function based methods, virtual equivalent system (VES) concept and methodology is adopted to address the stability issue of T-S model based fuzzy control systems. The stability of the VES is identical to that of the corresponding T-S model based fuzzy control system. The results developed in this paper indicate that the stability of T-S model based fuzzy control systems depends mainly on the following conditions: first, the local models cover the uncertainty of the plant to be controlled; second, the normalized membership function identifies the true model(s) of the plant, or the closest model(s) to the plant; third, each local controller stabilizes its corresponding local model.