In this thesis, the problem of stability for a largescale dynamical is primarily discussed with the unllator's criterion, the theory of this technique is based on the LaSale theorem (1.1) and Liqpunov's stability theorem. the main abvantage of this method is to simplify the given system of network, before the necessary and sufficient testing theorem is applied. We know that it is often possible to represent physical system by the input-output-state model, but for many processes (e.g. chemical plants, nuclear reactors), the order of the system may be quite large, and it is difficult to work with. A means of simplified system by nullator's criterion can be applied.
There are several main divisions of this thesis, chapter 2 is to rev the three ways of representation of a system and the relationships between them.
In chapter 3, there are three ways to represent a linear, time-ivnariant, positive real system, as system function H(s), state equation {A,B,C,D}, and {RLCTG} networks, and the relationships between them are presented.
In chapter 4, a new model, called a component-connection model is introduced and the relationships between the component-connection model and other representations are established.
Chapter 5 is to edvelop the nullator's criterion that is applied for linear, time-invariant, passive, portless {RLC} networks. An algorithm is described in detail for testing the stability of given {RLC} networks.
In Chapter 6, the stability analysis of the component-connection model is developed by use of the nullator's criterion, the algorithm of simplification of a given system is presented, and some examples are illustrated with the algorithm.
Chapter 7 is concern with the stability of the largescale dynamical system. A positive real component system transformed from a given general component system is discussed, and some basic equivalentstatements for the stability is presented and proved.
In chapter 8, the technique for testing stability of a system developed in chapters 6 and 7 is extended to the system containing linear time-varying memoryless components. Then the comparisons of our result wiht certain frequency domain criteria are described. Finally a possible extension to the nonlinear time-varying case is proposed.
In chapter 9, the results and conclusions are given.