On almost sure stability conditions of linear switching stochastic differential systems. (November 2016)

• Record Type: Journal Article
• Authors: Cong, Shen
• Is Part Of: Nonlinear analysis. Volume 22(2016)
• Page Start: 108
• Page End: 115
• Publication Date: 2016-11
• Subjects: Switching systems -- Stochastic systems -- Almost sure stability; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nahs.2016.03.010
• Languages: English
• ISSNs: 1751-570X

Abstract

Abstract: In modeling practical systems, it can be efficient to apply Poisson process and Wiener process to represent the abrupt changes and the environmental noise, respectively. Therefore, we consider the systems affected by these random processes and investigate their joint effects on stability. In order to apply Lyapunov stability method, we formulate the action of the infinitesimal generator corresponding to such a system. Then, we derive the almost sure stability conditions by using some fundamental convergence theorem. To illustrate the theoretical results, we construct an example to show that it is possible to achieve stabilization by using random perturbations.