Fuzzy controller design for Takagi–Sugeno fuzzy models with multiplicative noises via relaxed non-quadratic stability analysis

Abstract

In this paper, a relaxed non-quadratic stabilization analysis is developed to design fuzzy controllers for non-linear stochastic systems that are constructed by the Takagi–Sugeno (T–S) fuzzy models with multiplicative noises. The multiplicative noise term is introduced in the consequent part of the T–S fuzzy system for representing the stochastic behaviour. According to the proposed T–S fuzzy models, a relaxed non-quadratic technique is employed to derive the stability conditions for closed-loop fuzzy control systems. The relaxed non-quadratic stability conditions developed in this paper lead to the linear matrix inequality (LMI) problem. By solving the proposed LMI problem, the feasible solutions of the fuzzy control gains can be obtained. Finally, two numerical simulations are given to demonstrate the usefulness and applicability of the proposed fuzzy controller design approach.