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227-0225-00L 6 Credits DR , MSC D-MAVT , D-INFK , D-MATH , D-PHYS , D-ITET , D-BSSE

Linear System Theory

Lecturers & Examiners: Prof. Dr. John Lygeros, Dr. Anastasios Tsiamis

VVZ CR n/a

Last Updated: 2026-06-03 00:07:35

Abstract

The class is intended to provide a comprehensive overview of the theory of linear dynamical systems, stability analysis, and their use in control and estimation. The focus is on the mathematics behind the physical properties of these systems and on understanding and constructing proofs of properties of linear control systems.

Objective

Students should be able to apply the fundamental results in linear system theory to analyze and control linear dynamical systems.

Content

- Proof techniques and practices. - Linear spaces, normed linear spaces and Hilbert spaces. - Ordinary differential equations, existence and uniqueness of solutions. - Continuous and discrete-time, time-varying linear systems. Time domain solutions. Time invariant systems treated as a special case. - Controllability and observability, duality. Time invariant systems treated as a special case. - Stability and stabilization, observers, state and output feedback, separation principle.

Resources

Lecture Notes

Available on the course Moodle platform.

General Information

Language: English
Levels: DR , MSC
Frequency: Yearly recurring

Examination

Type: session examination
Mode: written 120 minutes
Aids: Four-page handwritten cheat sheet. Electronic aids are not allowed.

Additional credit will be available through graded exercises and an optional midterm examination. The midterm examination grade will be consolidated with the final examination grade (70% final, 30% midterm) only if it improves on the final grade. Exercise sets will be issued on a biweekly basis and contribute an additional 0.25 points to the grade of students who successfully complete 75% of the exercise sets.

Course Components

Type	Title	Time & Place	Hours
lecture with exercise	Linear System Theory	No time listed	5 h weekly

Offered In

Mechanical Engineering Master
- Core Courses (The Core Courses in the Master’s program Mechanical Engineering listed below are indicative and include courses designed by the Department at the Master's level. With the approval of the tutor, students may also select Master's-level courses offered by other departments at ETH. These courses will be marked as non-regular in the LAG, but their categorization as Core Courses is possible if included in the approved LAG.)
Computational Science and Engineering Master
- Fields of Specialization
  - Systems and Control
Micro- and Nanosystems Master
- Core Courses
  - Elective Core Courses
Computational Biology and Bioinformatics Master (More information at: )
- Advanced Courses (A total of 30 ECTS must be acquired in the advanced course category. Thereof, at least 16 ECTS in the theory and at least 10 ECTS in the biology subcategory.)
  - Theory (At least 16 ECTS need to be acquired in this subcategory.)
Electrical Engineering and Information Technology Master
- 01 - Courses of specializations
  - Tracks (all): Electives (This is only a short selection. Other courses from the ETH course catalogue may be chosen in agreement with your tutor. As an alternative to the elective courses, students may do a second semester project or an internship in industry. Please consult your tutor.)
  - Track: Systems and Control (The core courses and specialisation courses below are a selection for students who wish to specialise in the area of "Systems and Control", see . The individual study plan is subject to the tutor's approval.)
    - Core Courses (These core courses are particularly recommended for the field of "Systems and Control". You may choose core courses form other fields in agreement with your tutor. A minimum of 24 credits must be obtained from core courses during the MSc EEIT.)
      - Advanced Core Courses
  - Track: Signal Processing and Machine Learning (The core courses and specialisation courses below are a selection for students who wish to specialise in the area of "Signal Processing and Machine Learning ", see . The individual study plan is subject to the tutor's approval.)
    - Specialisation Courses (These specialisation courses are particularly recommended for the area of "Signal Processing and Machine Learning", but you are free to choose courses from any other field in agreement with your tutor. A minimum of 40 credits must be obtained from specialisation courses during the MSc EEIT.)
Robotics, Systems and Control Master
- Core Courses
Doctorate Information Technology and Electrical Engineering (A minimum of 12 ECTS credit points must be obtained during doctoral studies (also see sub-categories for details) More Information at )
- Subject Specialisation (The courses on offer below are only a small selection out of a much larger available number of courses. Please discuss your course selection with your PhD supervisor.)
Quantum Engineering Master
- Electives (This is a selection of courses particularly suitable for the MSc QE. In agreement with the tutor, students may choose other courses from the ETH course catalogue.)