Some properties of finite-time stable stochastic nonlinear systems

J. Yin, David Ding, Z. Liu and S. Khoo

Applied Mathematics and Computation, 2015, vol. 259, issue C, 686-697

Abstract: In this paper we study some properties of finite-time stable stochastic nonlinear systems. We begin by showing several continuous dependence theorems of solutions on initial values under some conditions on the coefficients of stochastic systems. We then derive some regular properties of its stochastic settling time for a finite-time stable stochastic nonlinear system. We show continuity, positive definiteness and boundedness of the expected stochastic settling time under appropriate conditions. Finally, a Lyapunov function is constructed by making use of the expectation of the stochastic settling time, and the infinitesimal generator of the stochastic system defined on the Lyapunov function is also given, and hence resulting in a converse Lyapunov theorem of finite-time stochastic stability.

Keywords: Finite-time stochastic stability; Stochastic nonlinear systems; Continuous dependence theorems; Stochastic settling time; Converse Lyapunov theorem (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:259:y:2015:i:c:p:686-697

DOI: 10.1016/j.amc.2015.02.088

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