Delay-range-dependent stability for uncertain stochastic systems with interval time-varying delay and nonlinear perturbations

Abstract

This paper considers the problem of robust stability for a class of uncertain stochastic systems with interval time-varying delay under nonlinear perturbations. A new delay-dependent method for robust stability of the systems is proposed. The innovation of the method includes employment of a tighter integral inequality and construction of an appropriate type of Lyapunov–Krasovskii functional. The restriction used to bound some trace term in the existing methods is also removed. The resulting criterion derived from this method has advantages over previous ones in that it has less conservatism and enlarges the scope of application. The reduction in conservatism of the proposed criterion is attributed to a method to estimate the upper bound on the stochastic differential of the Lyapunov–Krasovskii functional without neglecting any useful terms in the delay-dependent stability analysis. On the basis of the estimation and by utilizing free-weighting matrices, new delay-range-dependent stability criterion is established in terms of linear matrix inequality. Finally, numerical examples are provided to show the effectiveness and reduced conservatism of the proposed method.

Keywords:

• delay-range-dependent stability
• uncertain stochastic systems
• nonlinear perturbations

2000 AMS Subject Classifications :

• 34D10
• 93C10
• 93D09
• 93E03

Acknowledgements

This work was supported by Major Program of National Natural Science Foundation of China (no. 61134012), the 2011 Excellent Youth Project (no. Q20112907) of Hubei Provincial Department of Education.