Passivity based sliding mode control of uncertain singular Markovian jump systems with time-varying delay and nonlinear perturbations

In this paper, a sliding mode control (SMC) with passivity of uncertain singular Markovian jump systems (SMJS) with time-varying delay and nonlinear perturbations is investigated. Firstly, a new integral-type switching surface is designed. Secondly, by introducing free matrix method and Lyapunov functionals, a delay-dependent sufficient condition in terms of strict linear matrix inequalities (LMI) is derived for the resulting sliding mode dynamics such that the closed-loop system is stochastically admissible and robustly passive for all admissible uncertainties. Thirdly, a SMC law is synthesized to drive the system trajectories onto the predefined switching surface in a finite time. Finally, numerical examples are provided to demonstrate the effectiveness of the proposed method.