一般2-D线性常系数离散状态空间模型渐近稳定性的一类Lyapunov方法

A Lyapunov Method for Asymptotic Stability of a General 2-D State-Space Model for Linear Discrete Systems (2-D GM)

本文给出了一般2-D线性常系数离散状态空间模型(2-D GM)的渐近稳定性的定义以及相应的判据,并借助于Lyapunov方程给出了2-D Roesser Model(2-D RM)渐近稳定条件,推广和简化了文献[1,7]的有关结论。最后通过行列式的一个简单性质,证明了关于2-DGM渐近稳定性的判定可以转化为一类特殊的2-D RM的相应问题,从而得到了判定2-D GM渐近稳定性的Lyapunov方法。

In this paper, the definition of asymptotic stability and sufficient and necessary conditions for the stability of the general 2-D state space model for linear discrete systems(2-D GM) are given. In addition, neces-sary and sufficient conditions for asymptotic stability of Roesser model (RM) are presented based on the Lyapunov equation, also the results in [1,7] are extended. In the end, it is shown that the stability criteria for RM can be applied to a 2-D GM via a simple property of determinant of matrix, and then the stability of 2-D GM can be de-termined by that of RM. An example is given to illustrate the validity of the proposed mothod.