A sliding mode approach to stabilization of nonlinear Markovian jump singularly perturbed systems

This paper presents a sliding mode control (SMC) method for a class of nonlinear Markovian jump singularly perturbed systems (MJSPSs). The system is subject to parameter uncertainties and partly unknown transition probabilities. To fully employ the model characteristics of such a hybrid system, a novel integral-type switching function is firstly designed. By adopting the ε-dependent stochastic Lyapunov function method, sufficient conditions are presented to ensure the mean-square asymptotic stability of the sliding mode dynamics. A mode-dependent fuzzy SMC law is then synthesized to induce and maintain the sliding motion despite partly unknown transition probabilities and parameter uncertainties. Finally, the developed method is applied to stabilize a modified series DC motor system.