## Sliding mode control of singular stochastic hybrid systems.(English)Zbl 1193.93184

Summary: This paper is concerned with the Sliding Mode Control (SMC) of nonlinear singular stochastic systems with Markovian switching. An integral sliding surface function is designed, and the resulting sliding mode dynamics is a full-order Markovian jump singular stochastic system. By introducing some specified matrices, a new sufficient condition is proposed in terms of strict Linear Matrix Inequality (LMI), which guarantees the stochastic stability of the sliding mode dynamics. Then, a SMC law is synthesized for reaching motion. Moreover, when there exists an external disturbance, the $${\mathcal L}_2$$ disturbance attenuation performance is analyzed for the sliding mode dynamics. Some related sufficient conditions are also established.

### MSC:

 93E15 Stochastic stability in control theory 93E25 Computational methods in stochastic control (MSC2010) 60J75 Jump processes (MSC2010)
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### References:

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