Systems and Models

Abstract

As its title suggests, this book is about a special class of systems which in recent decades have become an integral part of our world. Before getting into the details of this particular class of systems, it is reasonable to start out by simply describing what we mean by a “system”, and by presenting the fundamental concepts associated with system theory as it developed over the years. This defines the first objective of this chapter, which is for the benefit of readers with little or no prior exposure to introductory material on systems and control theory (Sect. 1.2). Readers who are already familiar with concepts such as “state spaces”, “state equations”, “sample paths”, and “feedback” may immediately proceed to Sect. 1.3.

The second objective is to look at useful classifications of systems so as to reveal the features motivating our study of discrete event systems. Historically, scientists and engineers have concentrated on studying and harnessing natural phenomena which are well-modeled by the laws of gravity, classical and nonclassical mechanics, physical chemistry, etc. In so doing, we typically deal with quantities such as the displacement, velocity, and acceleration of particles and rigid bodies, or the pressure, temperature, and flow rates of fluids and gases. These are “continuous variables” in the sense that they can take on any real value as time itself “continuously” evolves. Based on this fact, a vast body of mathematical tools and techniques has been developed to model, analyze, and control the systems around us. It is fair to say that the study of ordinary and partial differential equations currently provides the main infrastructure for system analysis and control.