Course title
Topics in Mathematical Control

zhai guisheng Click to show questionnaire result at 2017
Course content
Lecture focusing on basic modelling, state behavior, stability analysis, controllability and observability, stabilizing and optimal state feedback, and observer (estimator) design of discrete-time linear systems.
Purpose of class
Basic on digital control systems analysis and design
Goals and objectives
  1. Understand modelling, state computation of continuous and discrete-time (CT/DT) systems
  2. Understand stability, controllability and observability of CT/DT systems
  3. Understand stabilizing and optimal state feedback, observer (estimator) design of CT/DT systems
Class schedule

Class schedule HW assignments (Including preparation and review of the class.) Amount of Time Required
1. Course introduction and basic knowledge on modern control Review of system modeling 190minutes
2. Laplace transform and transfer function Review of Laplace transform 190minutes
3. Continuous-time system analysis Review of ODE and its solutions 190minutes
4. Continuous-time system design Review of feedback control 190minutes
5. Z-transform, system modelling and transfer function Review of Z-transform and its properties 190minutes
6. System stability, Lyapunov stability theory Review of basic concept of convergence if system states 190minutes
7. Mid-term exam and review Review and prepare for mid-exam 190minutes
8. Controllability Review of matrix ranks 190minutes
9. State Feedback: stabilization Review of stability and matrix eigenvalues 190minutes
10. State Feedback: pole-assignment Review of stability and matrix eigenvalues 190minutes
11. Simulation Exercise with MATLAB/Simulink Refer to MATLAB manual 190minutes
12. Observability and dual system Review of matrix ranks, and consider the relation with controllability 190minutes
13. Observer design Think about the meaning of observers and its structure 190minutes
14. Optimal control Consider the meaning of cost functions and Riccati equations 190minutes
15. Final exam and overview
Total. - - 2660minutes
Relationship between 'Goals and Objectives' and 'Course Outcomes'

Exams Total.
1. 40% 40%
2. 30% 30%
3. 30% 30%
Total. 100% -
Evaluation method and criteria
Mid-term exam (40%) and final exam (60%)
Textbooks and reference materials
Basic knowledge on difference (differential) equation and matrices
Office hours and How to contact professors for questions
  • whenever the instructor is available
Relation to the environment
Non-regionally-oriented course
Development of social and professional independence
    Active-learning course
    Course by professor with work experience
    Work experience Work experience and relevance to the course content if applicatable
    N/A N/A
    Last modified : Thu Mar 21 15:39:57 JST 2019