State Feedback Control and Kalman Filtering with MATLAB/Simulink Tutorials

4Discrete‐time State Feedback Control

4.1 Introduction

The discrete‐time state feedback control systems share many similarities with their continuous‐time counterpart. However, they also have their own distinguishable features.

The chapter begins with the introduction of state feedback control in discrete‐time (see Section 4.2). Through a simple example, this section highlights the pole‐assignment controller design in discrete‐time and the selection of desired discrete‐time poles. Additionally, controllability in discrete‐time is explained in Section 4.2. In Section 4.3, the topics of observer and observability are covered. For a control system with multiple inputs or multiple outputs, the discrete‐time linear quadratic regulator (DLQR) provides both optimal controller and observer design, and this topic is discussed in Section 4.4. The topic of DLQR with a prescribed degree of stability is presented in Section 4.5 with case studies to illustrate its applications.

4.2 Discrete‐time State Feedback Control

4.2.1 Basic Ideas

Assume that a discrete‐time state space model is described by the difference equation:

(4.1)

where the state variable has dimension and the input variable ...