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Asymptotic Stabilizability of a Class of Stochastic Nonlinear Hybrid Systems

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  • Ewelina Seroka

Abstract

The problem of the asymptotic stabilizability in probability of a class of stochastic nonlinear control hybrid systems (with a linear dependence of the control) with state dependent, Markovian, and any switching rule is considered in the paper. To solve the issue, the Lyapunov technique, including a common, single, and multiple Lyapunov function, the hybrid control theory, and some results for stochastic nonhybrid systems are used. Sufficient conditions for the asymptotic stabilizability in probability for a considered class of hybrid systems are formulated. Also the stabilizing control in a feedback form is considered. Furthermore, in the case of hybrid systems with the state dependent switching rule, a method for a construction of stabilizing switching rules is proposed. Obtained results are illustrated by examples and numerical simulations.

Suggested Citation

  • Ewelina Seroka, 2015. "Asymptotic Stabilizability of a Class of Stochastic Nonlinear Hybrid Systems," International Journal of Stochastic Analysis, Hindawi, vol. 2015, pages 1-9, February.
    • Handle: RePEc:hin:jnijsa:231214
    DOI: 10.1155/2015/231214
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