Asymptotic Stabilizability of a Class of Stochastic Nonlinear Hybrid Systems | Zendy

Ewelina Seroka | Zendy

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Asymptotic Stabilizability of a Class of Stochastic Nonlinear Hybrid Systems

Author(s) -

Ewelina Seroka

Publication year - 2015

Publication title -

international journal of stochastic analysis

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.19

H-Index - 28

eISSN - 2090-3340

pISSN - 2090-3332

DOI - 10.1155/2015/231214

Subject(s) - mathematics , hybrid system , lyapunov function , nonlinear system , class (philosophy) , exponential stability , control theory (sociology) , state (computer science) , markov process , control (management) , computer science , artificial intelligence , statistics , physics , algorithm , quantum mechanics , machine learning

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

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