2025 (Current Year) Faculty Courses School of Engineering Undergraduate major in Systems and Control Engineering
Linear System Theory
- Academic unit or major
- Undergraduate major in Systems and Control Engineering
- Instructor(s)
- Mitsuji Sampei
- Class Format
- Lecture (Face-to-face)
- Media-enhanced courses
- -
- Day of week/Period
(Classrooms) - 3-4 Tue / 3-4 Fri
- Class
- -
- Course Code
- SCE.C301
- Number of credits
- 200
- Course offered
- 2025
- Offered quarter
- 1Q
- Syllabus updated
- Apr 1, 2025
- Language
- Japanese
Syllabus
Course overview and goals
This course covers the fundamentals of linear system theory based on state equations, and shows how to analyze systems and how to design controllers for them. In the system analysis, stability, controllability and observability are introduced. In the controller design, state feedback controllers (pole assignment and optimal control), observers and servo controllers are introduced.
The state equation is one of the system descriptions, and many kinds of systems can be described in state equations, for example, mechanical, electrical, chemical and economical systems. This course not only shows how to analyze and how to control systems, but also shows their theoretical background, which is necessary knowledge for developing new system theory.
Course description and aims
At the end of this course, students will be able to:
1) Analyze the stability, controllability and observability of the system.
2) Design stabilizing controllers.
3) Have an understanding of mathematical derivation of the theories, and acquire the ability to develop new system theory
Keywords
Linear System Theory, Linear Control Theory, State Equation.
Competencies
- Specialist skills
- Intercultural skills
- Communication skills
- Critical thinking skills
- Practical and/or problem-solving skills
Class flow
The first two thirds of the course concentrates on how to use theories. The remaining one third of the course gives the detailed mathematical proof of the theories.
Course schedule/Objectives
| Course schedule | Objectives | |
|---|---|---|
| Class 1 | System Modeling and State Equation | Describe linear systems using state equations. |
| Class 2 | Controllability | Check controllability of systems. |
| Class 3 | Observability | Check observability of systems. |
| Class 4 | Stability | Check stability of systems. |
| Class 5 | State Feedback: Pole Assignment | Design state feedback controllers using pole assignment method. |
| Class 6 | State Feedback: Optimal Control | Design state feedback controllers which minimize performance indexes. |
| Class 7 | Servo Controller and Internal Model Principle | Design servo controller. |
| Class 8 | Full Order Observer | Design full order observers for systems. |
| Class 9 | Kalman Filter and Duality | Design Kalman Filters for systems. |
| Class 10 | Lyapunov Function and Proof of Stability of Optimal Control | Explain the stability of the optimal control using Lyapunov function. |
| Class 11 | Proof of Optimality of Optimal Control Robustness and Asymptotic Characteristics of Optimal Control | Understand the proof of the optimal control. Explain the robustness and asymptotic characteristics of optimal control. |
| Class 12 | Disturbance Observer and Reduced Order Observer | Design disturbance observers and reduced order observers. |
| Class 13 | Stabilizability | Check stabilizability of systems. |
| Class 14 | Detectability | Check detectablilty of systems. |
Study advice (preparation and review)
To enhance effective learning, students are encouraged to spend approximately 100 minutes preparing for class and another 100 minutes reviewing class content afterwards (including assignments) for each class.
They should do so by referring to textbooks and other course material.
Textbook(s)
All materials used in class can be found on Science Tokyo LMS.
Reference books, course materials, etc.
K.J.Astrom and R.M.Murray: Feedback Systems: An Introduction for Scientists and Engineers, Princeton University Press
Evaluation methods and criteria
Students will be assessed on their understandings of system analysis (controllablity, observability, etc.) and controller design (state feedback, observer, etc.), and their ability to apply them to solve problems.
Students’ course scores are based on final exams (100%).
If the lecture should be conducted on line, course scores may be based on exercise problems and reports.
Related courses
- LAS.M102 ： Linear Algebra I / Recitation
- LAS.M106 ： Linear Algebra II
- SCE.C201 ： Fundamentals of Dynamical Systems
Prerequisites
Students must have successfully completed the followings or have equivalent knowledge.
LAS.M102 ： Linear Algebra I / Recitation
LAS.M106 ： Linear Algebra II
SCE.C201 ： Fundamentals of Dynamical Systems