Output Feedback Control of TS Fuzzy Systems with Unmeasured Nonlinearities via a Local Separation Principle

Abstract

This paper presents a fuzzy observer-based control framework for TS fuzzy models with nonlinear consequents (N-TS). The N-TS fuzzy model is constructed such that only measured nonlinearities are considered to obtain the fuzzy membership functions, and all unmeasured nonlinearities are modeled as local consequent parts. Based on the differential mean value theorem, the closed-loop system is rewritten in an adequate format, which allows proving the separation principle for asymptotic TS fuzzy observer-based control design. Sufficient design conditions, expressed in terms of linear matrix inequalities, are derived via delayed nonquadratic Lyapunov functions for the synthesis of both stabilizing fuzzy controller and Luenberger-like fuzzy observer. Using Lyapunov-based arguments of a local separation principle, a constructive procedure is provided to maximize the closed-loop domain of attraction (DoA) estimation, which is guaranteed to be included inside the predefined fuzzy modeling region. Numerical examples are given to illustrate the effectiveness of the proposed approach.