Lyapunov stability analysis of singular discrete large-scale systems
离散广义大系统的Lyapunov稳定性分析

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.