Delay-dependent robust stability of uncertain delayed stochastic systems: an LMI-based approach

In this paper we give a sufficient condition of delay dependent robust stability in terms of linear matrix inequalities (LMIs) for linear and nonlinear stochastic delayed systems with norm-bounded uncertainties. This type of dynamical system commonly resist in electronic, biological, and chemical systems. For delayed linear stochastic systems descriptor model transformation and corresponding Lyapunov-Krasovskii functional are adopted for stability analysis. Moreover, for delayed nonlinear stochastic systems usual model transformation and Lyapunov-Krasovskii functional suited for analysis of exponential stability is utilized. We show that our method is less conservative than other proposed methods numerically.