Introduction to State Space Theory

Abstract

State space theory deals with dynamical models describing both the internal dynamics of a given physical process and the interaction of the process with the outside world. In this chapter we introduce the general notion of a dynamical system and set the basis for the study of various important system classes. We emphasize that for us a dynamical system is a mathematical model and hence should be carefully distinguished from the physical process for which it is a model. Dynamical systems of different types may be used as models of one and the same physical process. Nevertheless it will sometimes be convenient to use the word “system” for the real physical process described by the dynamical model and in this case we shall add the epithet “real” or “physical” whenever this is necessary for a clear distinction.