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Zbl 1162.93044
Wu, Zhao-Jing; Xie, Xue-Jun; Shi, Peng; Xia, Yuan-Qing
Backstepping controller design for a class of stochastic nonlinear systems with Markovian switching. (English)
[J] Automatica 45, No. 4, 997-1004 (2009). ISSN 0005-1098

Summary: A more general class of stochastic nonlinear systems with irreducible homogeneous Markovian switching are considered in this paper. As preliminaries, the stability criteria and the existence theorem of strong solutions are first presented by using the inequality of mathematic expectation of a Lyapunov function. The state-feedback controller is designed by regarding Markovian switching as constant such that the closed-loop system has a unique solution, and the equilibrium is asymptotically stable in probability in the large. The output-feedback controller is designed based on a quadratic-plus-quartic-form Lyapunov function such that the closed-loop system has a unique solution with the equilibrium being asymptotically stable in probability in the large in the unbiased case and has a unique bounded-in-probability solution in the biased case.

MSC 2000:: *93E15 Stochastic stability
60J75 Jump processes
93B51 Design techniques in systems theory
93B52 Feedback control
60H10 Stochastic ordinary differential equations

Keywords: nonlinear stochastic systems; backstepping; Markovian switching

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