Abstract: The main contribution is to present stability analysis criterion for a type of norm⁃bounded uncertain perturbed discrete systems(NUPDS) with its states is subjected to a novel ellipsoidal outer approximation,which is different from the traditional bound description of general state. Based on the Lyapunov method, a delay dependent criterion and the corresponding state feedback control law, which are expressed in terms of linear matrix inequalities(LMIs) technology, are proposed to guarantee the asymptotic stability for the perturb delay systems. The solution of the LMIs can be obtained easily using existing efficient convex optimization techniques. A numerical example is given to illustrate effectiveness of the proposed method.

Key words: Discrete delay systems, Lyapunov method, Linear matrix inequalities, Ellipsoidal characteristic

摘要： 旨在针对一类范数有界不确定扰动离散系统提出稳定性分析判定标准。区别于传统的一般状态有界，该系统的状态受控于一种新颖的椭球外壳约束。基于李亚普诺夫方法，运用线性矩阵不等式技术表示出具有时滞的准则，给出了状态反馈控制律，保证了该类扰动时滞系统的渐近稳定性。这种线性矩阵不等式的评价标准，可以通过目前凸优化技术有效求解。数值例子表明了所提方法的有效性。

关键词: 离散时滞系统, 　李亚普诺夫方法, 　线性矩阵不等式, 　椭球特性