6Discrete‐Time Systems
6.1 Introduction
In this chapter we discuss discrete‐time systems, which are described by difference equations as opposed to the differential equations that we used to model continuous‐time systems. A general discrete‐time system is one of the form
The equation is autonomous if 
does not depend explicitly on 
. Discrete‐time systems arise in sampling of continuous‐time systems, in numerical integration and numerical optimization, signal processing, image processing, digital control, digital filtering, and other applications.
Examples
As a first example, consider the differential equation
Using the difference approximation for the derivative gives
Then, with 
and 
, we can approximate the differential equation (6.2) by the discrete‐time equation
Get Introduction to Modeling and Simulation now with the O’Reilly learning platform.
O’Reilly members experience books, live events, courses curated by job role, and more from O’Reilly and nearly 200 top publishers.
