Observer-based non-fragile H∞ control for discrete-time Takagi–Sugeno fuzzy systems

Abstract

Traditional methods frequently fail to address the coupling problem between control and observation gains in controller design, leading to increased complexity and conservatism in the design process. Moreover, in many practical scenarios, system state variables are often only partially observable, necessitating the development of output feedback-based controllers. This paper focuses on designing a non-fragile $H_{\infty }$ output feedback controller for discrete-time uncertain nonlinear systems, which are modeled using the Takagi–Sugeno (T–S) fuzzy framework. Given that the system states are only partially observable, a fuzzy observer is implemented to estimate the missing states. A Lyapunov function is constructed to derive the stability criterion for the augmented system, which is expressed by linear matrix inequalities (LMI). To tackle the dual coupling issue between control and observation gains, a novel decoupling method is introduced, leading to a co-design strategy. A practical example of the inverted pendulum is used to verify the potential and effectiveness of the proposed new design techniques.