Discrete-time Systems

Abstract

State-variable analysis has been developed entirely in terms of continuous systems, but the same principles and methods can be applied to discrete-time systems. In such systems, variables may change only at discrete intervals of time, the system being analogous to a difference equation. It may happen that portions of a system contain variables that change continuously, while other portions operate on a discrete basis. This situation arises when a continuous system such as a conventional servomechanism is operated by sampling a control signal, or when control information is obtained from a computer. Whatever the details of the system may be, the variables can be represented by a state vector, and the general methods developed previously can be used to investigate the system behaviour in terms of state-variable concepts similar to those for continuous systems.