Extended dissipative analysis for T–S fuzzy semi-Markov jump systems with sampled-data input and actuator fault

Abstract

This paper is concerned with reliable robust sampled-data control for T–S fuzzy semi-Markov jump systems (SMJSs) with time-varying delay. The asynchronous model is established, which makes the fuzzy sampled-data controller share the premise variable of the fuzzy plant with the fuzzy system. By adjusting the free weight matrix in the concept of extended dissipative, H∞, L2−L∞, passive and Q,S,R-dissipative performance are solved in a unified framework. A novel mode-dependent Lyapunov–Krasovskii functional (LKF) is constructed, which fully utilizes the characteristics of the real sampled period. Based on Lyapunov stability theory, Newton–Leibniz condition and new integral inequality techniques, some less conservative sufficient conditions are obtained to guarantee the close-loop system is stochastically stable and extended dissipative. Based on sampled-data approach, a robust reliable controller can be developed by solving the linear matrix inequalities (LMIs). The advantage and effectiveness of the proposed design method can be illustrated by the numerical example.