New results on delay-dependent stability analysis and stabilization for stochastic time-delay systems

This paper investigates the problems of stability analysis and stabilization for stochastic time-delay systems. Firstly, this paper uses the martingale theory to investigate expectations of stochastic cross terms containing the Ito integral. On the basis of this, an improved delay-dependent stability criterion is derived for stochastic delay systems. In the derivation process, the mathematical development avoids bounding stochastic cross terms, and neither model transformation method nor free-weighting-matrix method is used. Thus, the method leads to a simple criterion and shows less conservatism. Secondly, on the basis of this stability result, this paper further proposes a state-feedback controller that exponentially stabilizes the stochastic delay system by a strict LMI. Therefore, unlike previous results, it is not necessary to transform the nonlinear matrix inequalities into LMIs by the cone complementarity linearization method or parameter-tuning method, which always yield a suboptimal solution. Finally, examples are provided to demonstrate the reduced conservatism of the proposed conditions.Copyright (c) 2013 John Wiley & Sons, Ltd.