Asymptotic Stabilizability of a Class of Stochastic Nonlinear Hybrid Systems

Ewelina Seroka

International Journal of Stochastic Analysis, 2015, vol. 2015, 1-9

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.

Date: 2015
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnijsa:231214

DOI: 10.1155/2015/231214

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