Robust exponential stability criteria of uncertain stochastic systems with time-varying delays

This article may be used for research, teaching and private study purposes. Any substantial or systematic reproduction, redistribution , reselling , loan or sub-licensing, systematic supply or distribution in any form to anyone is expressly forbidden. The publisher does not give any warranty express or implied or make any representation that the contents will be complete or accurate or up to date. The accuracy of any instructions, formulae and drug doses should be independently verified with primary sources. The publisher shall not be liable for any loss, actions, claims, proceedings, demand or costs or damages whatsoever or howsoever caused arising directly or indirectly in connection with or arising out of the use of this material. This article investigates the problem of delay-dependent exponential stability in mean square for continuous-time linear stochastic systems with structured uncertainties and time-varying delays. By applying descriptor model transformation of the systems, a new type of Lyapunov–Krasovskii functional is constructed, and by introducing some free weighting matrices, some new delay-dependent and delay-independent stability criteria are derived respectively in terms of an LMI algorithm. The new stability criteria are less conservative than existing results. Numerical examples demonstrate that the new criteria are effective and are an improvement over existing results. 1. Introduction During the last few decades, many authors have investigated the robust stability analysis of dynamic systems with delays. In general, delay-dependent stability criteria make use of the information on the size of delays, they are less conservative than delay-independent ones, especially for small delays. Therefore, much interest has been focused on the delay-dependent stability analysis of delay systems (see, e.g. have discussed the delay-dependent stability for stochastic systems with delays. Verriest and Florchinger (1995) presented the stability of a linear stochastic differential equation via Riccati equations. gave the delay-dependent robust stability criteria of uncertain stochastic systems. However, the criteria given in Yue and Won (2001) involved the parameterised model transformation