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

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Linear System Theory

Lecturers & Examiners: Dr. Marcello Colombino

VVZ CR n/a

Last Updated: 2026-02-05 15:35:50

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: Two page handwritten cheat sheet.

Addtional credit will be available through graded exercises and an optional take-home 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 weekly 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 The lecturers will communicate the exact lesson times of ONLINE courses.	Mon 09:00-12:00 (ON LI NE) Wed 10:00-12:00 (ON LI NE)	5 h weekly

Offered In

Mechanical Engineering Master
- Core Courses
  - Robotics, Systems and Control (The courses listed in this category “Core Courses” are recommended. Alternative courses can be chosen in agreement with the tutor.)
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 informations at: )
- Advanced Courses (A total of 30 ECTS needs to be acquired in the Advanced Courses category. Thereof 18 ECTS in the Theory and 12 ECTS in the Biology category. Note that some of the lectures are being recorded: )
  - Theory (At least 18 ECTS need to be acquired in this category.)
Electrical Engineering and Information Technology Master
- Master Studies (Programme Regulations 2018)
  - Energy and Power Electronics (The core courses and specialisation courses below are a selection for students who wish to specialise in the area of "Energy and Power Electronics", see . The individual study plan is subject to the tutor's approval.)
    - Specialisation Courses (These specialisation courses are particularly recommended for the area of "Energy and Power Electronics", 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 Master's Programme.)
  - 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 (Advanced core courses bring students to gain in-depth knowledge of the chosen specialization. They are MSc level only.)
  - 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.)
- Master Studies (Programme Regulations 2008)
  - Major Courses (A total of 42 CP must be achieved during the Master Programme. The individual study plan is subject to the tutor's approval.)
    - Energy and Power Electronics
      - Recommended Subjects (These courses are recommended, but you are free to choose courses from any other special field. Please consult your tutor.)
    - Systems and Control
      - Core Subjects (These core subjects are particularly recommended for the field of "Systems and Control".)
    - Signal Processing and Machine Learning
      - Recommended Subjects
Robotics, Systems and Control Master
- Core Courses
Doctoral Dep. of Information Technology and Electrical Engineering (More Information at: )
- Doctoral and Post-Doctoral Courses (A minimum of 12 ECTS credit points must be obtained during doctoral studies. 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.)