Reliable mixed H∞/passive control for T-S fuzzy delayed systems based on a semi-Markov jump model approach

This paper investigates the problem of the reliable mixed H∞/passive control for Takagi-Sugeno (T-S) fuzzy delayed systems based on a semi-Markov jump model (SMJM) approach. The focus is to design a fuzzy fault-tolerant controller such that the resulting closed-loop system is stochastically stable with a prescribed mixed H∞/passive performance level even if the actuator failures appear. A semi-Markov process is employed to describe the encountered failures of the actuator. By applying the Lyapunov-Krasovskii method, in combination with some novel inequalities, some conditions on the performance analysis are established, where some negative quadratic terms are fully considered to reduce the conservatism. Based on the conditions, an explicit expression for the desired controller is given. Three numerical examples are presented to show the effectiveness and reduced conservatism of the proposed method.