On Delay-Dependent Stability for a Class of Discrete Nonlinear Stochastic Systems

Authors:	Basin Michael, Autonomous University of Nuevo Leon, Mexico Rodkina Alexandra, University of the West Indies, Jamaica
Topic:	1.4 Stochastic Systems
Session:	Control, Estimation and Analysis of Stochastic Systems
Keywords:	Discrete stochastic time-delay system, asymptotic stability, Lyapunov-Krasovskii and degenerate functionals, martingale convergence theorems

Abstract

Global asymptotic stability conditions for discrete nonlinear scalar stochastic systems with state delayare obtained based on the convergence theorem for semimartingale inequalities, without assuming the Lipschitz conditions for nonlinear drift functions. The Lyapunov-Krasovskii and degenerate functionals techniques are used. The derived stability conditions are directly expressed in terms of the systemcoefficients. The obtained results are compared to some previously known asymptotic stability conditions for discrete nonlinear stochastic systems.