Observer-based mixed H∞ and passive control for T-S fuzzy semi-Markovian jump systems with time-varying delay via sliding mode method

This article presents the subject of the Takagi-Sugeno fuzzy sliding mode approach for nonlinear semi-Markovian modedependent delay switching systems. In addition, the mixed H-infinity/passive performance was considered. The non-fragile observer is introduced to reconstruct variables, such that the error dynamics are obtained. By raising a novel fuzzy integral sliding surface function on the probability space, the new closed-loop sliding mode dynamic constitutes by observer and estimate systems satisfies both the mixed H-infinity/passive performance index and the stochastic stable as the new model-dependent Lyapunov-Krasovskii function is established. Moreover, sufficient conditions are carried out based on linear matrix inequality (LMI), which ensures the results of our work can be verified by the feasibility problem in terms of LMI. Then the sliding mode control is designed to make the system's trajectory reach the predefined sliding surface. Finally, four numerical examples are given to testify the availability and less conservatism of the theoretical method.