State Feedback Control and Kalman Filtering with MATLAB/Simulink Tutorials

3Introduction to Discrete‐time Systems

3.1 Introduction

As we have learned from the previous chapters, the continuous‐time control systems are very efficient in controlling the physical systems that have a fast sampling rate because they are designed in the continuous‐time and implemented in the discrete‐time, where an approximation due to the discretization is accepted in the implementation stage. Furthermore, the existence of a continuous‐time model underpins the development of continuous‐time control systems.

In the digital world, the physical models are often naturally presented in terms of sampled data. These systems commonly operate in a slower sampling environment, and it is difficult to describe them using differential equations in continuous‐time due to information losses from the slow sampling rate. For these types of systems, it is natural to describe their dynamics using difference equations and design control systems in discrete‐time. Designing the control systems in discrete‐time presents advantages when continuous‐time physical systems have a limited sampling rate. Because the discrete‐time systems are more naturally connected to real world data, it is relatively easier to handle the systems with communication delays, missing data and multi‐rate sampled data systems.

For those who are not familiar with discrete‐time systems, the introductory materials presented in this chapter give a starting point. The chapter begins with the discretization of a continuous‐time ...