This course provides important mathematical results on discrete-time linear systems based on state-space equations, especially for the stability/performance analysis and controller/observer synthesis.

The contents and keywords are as follows.

1. Introduction

2. Mathematical Preliminaries

• z transform, linear algebra

3. Discrete-Time State-Space Equations

• Basic concepts of state-space equations

• Solutions to linear differential equations

• Frequency response

4. Properties of Discrete-Time Systems

• Stability, Lyapunov stability theorem

• Reachability, controllability, stabilizability

• Observability, constructability, detectability

• PBH test 

5. Discretization of Continuous-Time Systems

• ZOH discretization

• Properties of discretized systems 

• Nonpathological sampling period

• Impulse modulation theorem

• Aliasing and sampling theorem  

6. Controller/Observer Synthesis

• Pole placement control

• Linear quadratic regulator

• Luenberger observer

• Kalman filter

7. Sampled-Data Synthesis

• Sampled-data optimal regulator

• Sampled-data H2 optimal control