On exponential stability conditions of linear neutral stochastic differential systems with time-varying delay


Correspondence to: S. Cong, School of Mechanical and Electrical Engineering, Heilongjiang University, Harbin 150080, China.

E-mail: shen_tsong@yahoo.com.cn


We consider a class of neutral stochastic systems with time-varying delay and study the exponential stability in the mean square sense. We derive sufficient stability conditions via applying Lyapunov functional method along with some practical techniques. Firstly, in computing the constructed Lyapunov functional, we make use of some basic rules of Itô calculus to reduce the conservatism produced by noise because it, in principle, plays a negative role for preserving stability in the mean square sense. Also, it is an important observation that, using some slack matrices, we can create convex conditions to accommodate the computation to time-varying delay. In the sequel, we use a perturbation approach to estimate the decay rate of state and come to the conclusion of stability. Finally, we include an example to demonstrate the effectiveness of the method. Copyright © 2012 John Wiley & Sons, Ltd.