中立型灰色随机分布时滞系统的指数鲁棒稳定性

Exponential Robust Stability of Grey Neutral Stochastic Systems with Distributed Delays

为了得到一类中立型灰色随机分布时滞系统的指数鲁棒稳定性,本文利用Lyapunov-Krasovskii泛函法、灰矩阵的连续矩阵覆盖的分解技术和Ito公式,分别得到了以非线性矩阵不等式和线性矩阵不等式(LMI)表示的该系统指数鲁棒稳定的时滞依赖性判据。对非线性矩阵不等式判据,我们给出了一般性算法,解决了非线性矩阵不等式判据不便于实际应用的问题。数值例子表明,本文所给判据是有效的,且系统的指数稳定性和时滞,随着绝对灰度矩阵的谱范数的增大而减小。

In this paper, we investigate the exponential robust stability for a class of grey neutral stochastic systems with distributed delays. By constructing the Lyapunov-Krasovskii functional and applying the decomposition technique of continuous matrix-covered sets of grey matrix and the Ito formula, the delay-dependent criteria for exponential robust stability are formulated in the forms of non-linear matrix inequalities and linear matrix inequalities, respectively. A generic algorithm for the non-linear matrix inequalities is given. The existent criteria for non-linear matrix inequalities are not convenient for applications in practice, and our algorithm solves this problem. Numerical examples demonstrate the e？ectiveness of the presented criteria, and that the exponential stability and time-delay of systems decrease as the spectral norm of the absolute grey-degree matrix increases.