离散广义大系统的Lyapunov稳定性分析

广义大系统的稳定性是广义大系统理论的基本问题之一,对其稳定性的研究要比状态空间大系统复杂得多,因为广义大系统不仅需要考虑稳定性,而且还要考虑正则性和因果性(离散广义系统)及脉冲自由(连续广义系统).本文在所有孤立子系统都是正则的且具有因果关系的条件下,利用Lyapunov方程,应用Lyapunov函数方法,研究了广义离散线性大系统和广义离散非线性大系统的稳定性和不稳定性问题,给出了离散广义大系统稳定性和不稳定性判定定理,得到了离散广义大系统的关联稳定参数域和不稳定域.

Lyapunov stability analysis of singular discrete large-scale systems

Asymptotic stability is one of the fundamental problems in the theory of singular large-scale systems. Its determination is more complicated than that for nonsingular large-scale systems in state-space form, because for singular large-scale systems one has to consider not only stability but also regularity and impulse immunity (for continuous singular systems) and causality (for discrete singular systems). In this paper the problem of asymptotic stability and instability for the singular discrete linear large-scale systems and singular discrete non-linear large-scale systems is investigated by the method of Lyapunov equation and Lyapunov function. Under the condition that all isolated subsystems are regular and causal, the criteria are given to determine whether or not the discrete singular large-scale system is asymptotically stable or unstable. The interconnecting parameter regions of asymptotic stability and instability for the system are obtained as well.