Robust H∞ Control for Markovian-Jump-Parameters Takagi–Sugeno Fuzzy Systems

Abstract

The $H_{\infty }$ performance of a class of T-S fuzzy systems with Markovian-jump parameters is analyzed. A state feedback controller is designed for T-S fuzzy systems with Markovian-jump parameters. First, a new modal-dependent Lyapunov function composed of closed-loop functions is constructed, which can fully use system status information. Based on this function, the stability conditions with less conservatism are given by linear matrix inequalities (LMIS). At the same time, a design algorithm for a state feedback controller is proposed for the Markovian-jump-parameters T-S fuzzy systems, which ensures the system’s stability under the condition of $H_{\infty }-\gamma$ performance. Simulation results demonstrate that the mentioned method is accurate and practical.