Linear Control System Can Be Distinguished

In recent years, both control and computer science have been attracted by hybrid systems. They provide a unified framework for describing processes evolving according to continuous dynamic, discrete dynamics, and logic rules. When we consider the control problems of the hybrid systems, we found that some problems that never appeared in the classic control theory came out. For example, we must solve the distinguishablity related to linear control systems, before we research the observability of hybrid systems. As to the distinguishability, it has been used in many fields for long time with different meanings in control theory, but they are usually not well-defined. Moreover for many cases, the necessary and sufficient conditions to guarantee the distinguishability also remains open. In this paper we will give some definitions of the distinguishability, and also conclude some necessary and sufficient conditions for distinguishability. We think that these results will be helpful in considering the observability of hybrid systems.This paper divided to three chapters. Chapter 1 is the exordium; In chapter 2, we give some definitions of the distinguishability, and have introduced some other auxiliary definitions, we also give some conclusions about these different distinguishabilities. Finally we have given some generalized conclusions; In chapter 3 we consider the observability of hybrid systems which is under some given running model.