Exponential stability criteria for uncertain stochastic systems

This paper considers the problem of delay-dependent exponential stability in mean square for a class of stochastic systems with polytopic-type uncertainties and time-varying delay. Based on the application of the descriptor model transformation and free weighting matrices to express this relationship among the system variables and among the terms in the Newton-Leibniz formula, some new delay-dependent exponential stability criteria are obtained in terms of linear matrix inequalities (LMIs). The new criteria are less conservative than existing ones. Numerical examples demonstrate the new criteria are effective and are an improvement over existing ones.