Reliable Finite-Time H ∞ Control for T–S Fuzzy Semi-Markovian Jump Delay Systems

This paper addresses the observer-based finite-time $$H_{\infty }$$ control problem for Takagi–Sugeno (T–S) fuzzy semi-Markovian jump systems with mode-dependent fast-varying delays, actuator faults, parameter uncertainties and partly uncertain transition rates. Firstly, a more general actuator fault model is considered and the fuzzy reliable observer-based control scheme is designed. By applying the new Lyapunov functional candidates, free-weighting matrix method and slack matrix variables, some negative integral terms can be adopted and the nonlinear terms caused by time delay and partly unknown transition rates can be dealt. Furthermore, novel sufficient conditions on guaranteeing the closed-loop system is stochastically finite-time bounded (SFTB) with the prescribed $$H_{\infty }$$ level are proposed. Particularly, different from traditional slowly varying delays, the case of mode-dependent fast-varying delays which are more difficult to be dealt is considered in this paper. Lastly, a practical example is exploited to affirm the validity of the obtained results.