On exponential stability conditions of linear neutral stochastic differential systems with time‐varying delay
On exponential stability conditions of linear neutral stochastic differential systems with time‐varying delay
复制标题
DOI：
10.1002/rnc.2818
复制
发表时间：
2013-07
影响因子：
3.9
通讯作者：
S. Cong
中科院分区：
文献类型：
--
作者：
S. Cong
考虑一类具有时变时滞的中立型随机系统，研究其均方意义上的指数稳定性。利用李雅普诺夫泛函方法，结合一些实用技术，给出了充分的稳定性条件。首先，在计算构造的Lyapunov泛函时，我们利用Itô微积分的一些基本规则来降低噪声产生的保守性，因为原则上，噪声在均方意义上对保持稳定性起负作用。此外，一个重要的观察结果是，使用一些松弛矩阵，我们可以创建凸条件来适应时变延迟的计算。在第二部分中，我们用摄动方法估计了状态的衰减率，并得出了稳定的结论。最后，通过实例验证了该方法的有效性。版权所有©2012 John Wiley & Sons， Ltd。
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.