Stability of Singularly Perturbed Stochastic Systems with Discrete and Distributed Delays

Abstract

The problems of stability for a class of the singularly perturbed stochastic systems with discrete and distributed delays are studied. By using a Lyapunov–Krasovskii functional approach and terms of linear matrix inequalities (LMIs), stability in mean square criteria ensuring asymptotically stability of the singularly perturbed stochastic systems with discrete and distributed delays are established. New asymptotically stable in mean square criteria for the singularly perturbed stochastic systems with time-varying delay are obtained as well. Finally, the validity of the obtained results is shown by a numerical example.