Observer-Based Robust $H_{\infty }$ Reliable Control for Uncertain T–S Fuzzy Systems With State Time Delay

Abstract

In this paper, a method of robust H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> reliable control for uncertain Takagi-Sugeno (T-S) fuzzy systems with unavailable states and time-varying delay is developed. In terms of linear-matrix inequalities (LMIs), we derive sufficient conditions for the existence of the fuzzy observer and the reliable fuzzy controller. The single-step LMI conditions, depending on the size of the delay, are proposed for the observer-based H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> reliable controller design. This overcomes the drawback of two-step LMI approach in literature. Moreover, the designed fuzzy controller is reliable in the sense that the stability and the satisfactory performance of the closed-loop system are achieved not only under normal operation but in the presence of some actuator faults as well. The result is given without the assumption of the rate of change of time-delay function (i.e., |τ̊| <; 1), which makes it applicable to both slow and fast time-varying delayed systems. Without considering reliability, the proposed result is much less conservative than most of the existing results. Finally, several examples are given to show the effectiveness and advantages of our results.