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Automatica, Vol.97, 404-413, 2018
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 epsilon-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. (C) 2018 Published by Elsevier Ltd.