Finite-time stability and stabilization of nonlinear stochastic hybrid systems

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Abstract

This paper deals with the problem of finite-time stability and stabilization of nonlinear Markovian switching stochastic systems which exist 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.

Keywords

Finite-time stability
Impulsive systems
Markovian switching
Brownian motion
Stabilization

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This work was partially supported by the National Natural Science Foundations of China (60374015).