线性离散大系统稳定性的部分分解法

Partial Decomposition of Linearly Large-Scale Discrete Systems in Stability

该文研究子系统间具有强耦合的线性离散大系统的稳定性。提出一种适合于该类大系统稳定性分析的部分分解法。该方法可将高阶线性离散大系统化为若干个具有单向解耦的低阶子系统来研究。从而 ,利用标量李雅普诺夫函数将高阶矩阵李雅普诺夫方程化为若干个单向解耦的低阶矩阵方程。通过线性矩阵不等式得到线性离散大系统稳定性的充分条件。

In this paper,the stability of linearly time-invariant large-scale discrete systems with strong coupling in a single direction among subsystems is considered.A partial decomposing method is proposed.By using the method, a linearly timeinvariant large-scale discrete system can be decomposed into some decouplign subsystems in a single direction.Then a higher order Lyapunov matrix equation can be transformed into some lower order matrix equations with coupling in a single direction by scalar Lyapunov function.The sufficient conditions of stability are obtained by matrix inequalities.