Table of Contents
International Journal of Stochastic Analysis
Volume 2015, Article ID 231214, 9 pages
Research Article

Asymptotic Stabilizability of a Class of Stochastic Nonlinear Hybrid Systems

Faculty of Mathematics and Natural Sciences, College of Sciences, Cardinal Stefan Wyszyński University in Warsaw, Dewajtis Street 5, 01-815 Warsaw, Poland

Received 23 August 2014; Accepted 7 January 2015

Academic Editor: Henri Schurz

Copyright © 2015 Ewelina Seroka. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.