A sliding mode approach to stabilization of nonlinear Markovian jump singularly perturbed systems. (English) Zbl 1406.93370
Summary: 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 \(\varepsilon\)-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.
MSC:
| 93E15 | Stochastic stability in control theory |
| 93B12 | Variable structure systems |
| 93D20 | Asymptotic stability in control theory |
| 93C70 | Time-scale analysis and singular perturbations in control/observation systems |
| 93C42 | Fuzzy control/observation systems |
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