Robust Stability Analysis of TS-Fuzzy-Model-Based Control Systems with Both Elemental Parametric Uncertainties and Norm-Bounded Approximation Error

Abstract

This paper discusses the robust stability of Takagi-Sugeno (TS) fuzzy model based control systems. First, it is pointed out that the complex nonlinear control systems with uncertain parameters can be represented as the TS-fuzzy-model-based control systems with both elemental parametric uncertainties and norm-bounded approximation error. Next, a sufficient condition is proposed in terms of linear matrix inequalities (LMIs) for ensuring that the TS-fuzzy-model-based control systems with both elemental parametric uncertainties and norm-bounded approximation error are robustly stable. Some examples are given to show that the proposed sufficient LMI condition may obtain less conservative results than the existing ones reported recently, owing to the proposed sufficient condition taking the elemental information of the parametric uncertain matrices into consideration.