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Sliding mode control for Itô stochastic systems with Markovian switching. (English) Zbl 1119.93063
Summary: This paper deals with the problem of sliding mode control (SMC) for a class of nonlinear uncertain stochastic systems with Markovian switching. By introducing some specified matrices, the connections among the designed sliding surfaces corresponding to every mode are established. Furthermore, the present sliding mode controller including the transition rates of modes can cope with the effect of Markovian switching. By means of linear matrix inequalities (LMIs) with equality constraint, sufficient conditions are derived such that the sliding motions on the specified sliding surfaces are stochastically stable with $\gamma$-disturbance attenuation level. Finally, a numerical example is given to illustrate the applicability of the present method.

##### MSC:
 93E03 General theory of stochastic systems 60H10 Stochastic ordinary differential equations 93B12 Variable structure systems 93E15 Stochastic stability
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##### References:
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