## Sliding mode control of switched hybrid systems with stochastic perturbation.(English)Zbl 1236.93038

Summary: This paper is concerned with the sliding mode control (SMC) of a continuous-time switched stochastic system. A sufficient condition for the existence of reduced-order sliding mode dynamics is derived and an explicit parametrization of the desired sliding surface is also given. Then, a sliding mode controller is then synthesized for reaching motion. Moreover, the observer-based SMC problem is also investigated. Some sufficient conditions are established for the existence and the solvability of the desired observer and the observer-based sliding mode controller is synthesized. Finally, numerical examples are provided to illustrate the effectiveness of the proposed theory.

### MSC:

 93B12 Variable structure systems 93C30 Control/observation systems governed by functional relations other than differential equations (such as hybrid and switching systems)
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### References:

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