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Finite-time stability and stabilization of nonlinear stochastic hybrid systems. (English) Zbl 1163.93033
Summary: This paper deals with the problem of finite-time stability and stabilization of nonlinear Markovian switching stochastic systems which have impulses at the switching instants. Using multiple Lyapunov function theory, a sufficient condition is established for finite-time stability of the underlying systems. Furthermore, based on the state partition of continuous parts of systems, a feedback controller is designed such that the corresponding impulsive stochastic closed-loop systems are finite-time stochastically stable. A numerical example is presented to illustrate the effectiveness of the proposed method.

MSC:
93E03General theory of stochastic systems
93E15Stochastic stability
60J75Jump processes
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References:
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