Non-fragile Observer-Based $${\varvec{H_\infty}} $$ Control for Switched Takagi–Sugeno Fuzzy Systems Using Past Output Measurements

Abstract

This paper pays attention to the non-fragile observer-based \(H_\infty \) control problem of switched Takagi-Sugeno (T–S) fuzzy systems, where every subsystem is described by the T–S fuzzy model with local nonlinear terms. Different from the existing observer-based control strategy, a distinguishing feature of this paper is that constructed observers can make full use of current and past output measurements to enhance the performance of the observers in state estimation. However, the introduction of past output measurements has brought challenges to stability analysis and controller design. To tackle these difficulties and design a set of non-fragile fuzzy controllers to stabilize the systems, a new augmented state vector is constructed. First, a new non-fragile observer-based \(H_\infty \) control criterion is deduced based on the fuzzy Lyapunov function method. Then, the method of simultaneously solving observer and controller gains is obtained by introducing free matrix variables and using the linear matrix inequality approach. This solving method is more efficient than the traditional two-step method. Finally, two confirmatory instances are given.