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On exponential stability conditions of linear neutral stochastic differential systems with time-varying delay. (English) Zbl 1271.93162

Summary: 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.

MSC:

93E12 Identification in stochastic control theory
93E03 Stochastic systems in control theory (general)
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
93C05 Linear systems in control theory
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