一类离散时滞随机系统的稳定性分析

Stability Analysis of a Class of Discrete Stochastic Systems with Time-delays

针对一类不确定随机离散变时滞系统,建立了随机稳定性标准,该系统中随机干扰满足布朗运动。选取合适的李雅普诺夫函数,借助于随机稳定性理论、自由权矩阵和线性矩阵不等式等方法,给出并证明了使得该系统随机稳定的充分条件,所有结果以线性矩阵不等式的形式给出,应用例子和仿真表明所给稳定性标准的有效性。

The standards of delay-dependent stability are established for a class of discrete stochastic systems with time delays, and the stochastic perturbation is described in term of a Brownian motion. Based on proper Lyapunov-Krasovskii functional, and by means of the stochastic stability theory, the free-weight matrix and the linear matrix inequalities, the sufficient conditions which make discrete stochastic systems with time delays stable were provided and proved. All results were given in terms of the linear matrix inequalities. Numerical examples and simulations were given to illustrate the effectiveness of the proposed method.