TABLE OF CONTENTS In Section 1.10, basic notions of state variables were introduced. In this chapter, we shall discuss state variables in more depth.
Most of this book deals with external (input-output) description of systems. As noted in Chapter 1, such a description may be inadequate in some cases, and we need a systematic way of finding a system's internal description. State-space analysis of systems meets this need. In this method, we first select a set of key variables, called the state variables, in the system. Every possible signal or variable in the system at any instant t can be expressed in terms of the state variables and the input(s) at that instant t. If we know all the state variables as a function of t, we can determine every possible signal or variable in the system at any instant with a relatively simple relationship. The system description in this method consists of two parts:
A set of equations relating the state variables to the inputs ( the state equation).
A set of equations relating outputs to the state variables and the inputs ( the output equation).
The analysis procedure, therefore, consists of solving the state equation first, and then solving the output equation. The state-space description is capable of determining every possible system variable (or output) from knowledge of the input and the initial state (conditions) of the system. For this reason, it is an internal description of the system.
By its...
