Robust H∞$$ {H}_{\infty } $$ Sliding Mode Control for One‐Sided Lipschitz T‐S Fuzzy Singular Semi‐Markovian Jump Systems With Time‐Varying Delay

ABSTRACT This work investigates the robust sliding mode control (SMC) law design for uncertain T‐S fuzzy singular semi‐Markovian jump systems (S‐SMJSs) with time‐varying delays and one‐sided Lipschitz (OSL) nonlinearities. A fuzzy integral sliding mode surface (SMS) is designed. Then, given that the modeling of general fuzzy systems struggles to approximate the complex nonlinearities in practical systems, this work addresses more general nonlinearities considering the T‐S fuzzy strategy, the OSL condition, and the quadratically inner‐bounded (QIB) condition. A mode‐dependent Lyapunov function is designed, and sufficient conditions of stochastic admissibility are derived for the sliding motion with performance by using a novel matrix constraint condition and a scaling approach, which have lower conservatism. Moreover, an appropriate SMC law is proposed, which can satisfy the reachability condition and keep the sliding motion admissible under the disturbances and nonlinearities. Finally, the effectiveness of the results is validated by four examples.