Abstract
A sufficient condition is presented for the overall stability of large scale interconnected system with zero input. In this paper it is assumed that the overall behavior of interconnected system is determined only by the outputs of subsystems. The concept of macroscopic stability is introduced from this point of view.
So far, several results have been obtained on this problem making use of a Liapunov function for each subsystem. However, to construct Liapunov functions, differential equations must be presented for each subsystem. Moreover, even if differential equations are given, the construction of Liapunov functions is in general not easy.
To overcome these difficulties, a simple method is presented for describing the dynamic relation between the input and the output of a subsystem.
With this description of the dynamics of each subsystem, a sufficient condition is given for the macroscopic stability of interconnected systems. This condition dose not neccessarily contain all the results obtained so far, but it can be applied not only to finite dimensional systems but also to time-delay systems.
