p-Stability andp-Stabilizability of Stochastic Nonlinear and Bilinear Hybrid Systems under Stabilizing Switching Rules | Zendy

Ewelina Seroka | Zendy; L. Socha | Zendy

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p-Stability andp-Stabilizability of Stochastic Nonlinear and Bilinear Hybrid Systems under Stabilizing Switching Rules

Author(s) -

Ewelina Seroka,

L. Socha

Publication year - 2013

Publication title -

journal of applied mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.307

H-Index - 43

eISSN - 1687-0042

pISSN - 1110-757X

DOI - 10.1155/2013/206190

Subject(s) - algorithm , stability (learning theory) , function (biology) , mathematics , lyapunov function , exponential function , computer science , machine learning , mathematical analysis , nonlinear system , physics , quantum mechanics , evolutionary biology , biology

The problem of pth mean exponential stability and stabilizability of a class of stochastic nonlinear and bilinear hybrid systems with unstable and stable subsystems is considered. Sufficient conditions for the pth mean exponential stability and stabilizability under a feedback control and stabilizing switching rules are derived. A method for the construction of stabilizing switching rules based on the Lyapunov technique and the knowledge of regions of decreasing the Lyapunov functions for subsystems is given. Two cases, including single Lyapunov function and a a single Lyapunov-like function, are discussed. Obtained results are illustrated by examples

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