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.
Learning 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.
Lecture notes
Available on the course Moodle platform.
Prerequisites / Notice
Sufficient mathematical maturity, in particular in linear algebra, analysis.
Competencies
Subject-specific Competencies
Concepts and Theories
assessed
Techniques and Technologies
assessed
Method-specific Competencies
Analytical Competencies
assessed
Problem-solving
assessed
Personal Competencies
Creative Thinking
fostered
Critical Thinking
fostered
Integrity and Work Ethics
fostered
Performance assessment
Performance assessment information (valid until the course unit is held again)
The performance assessment is only offered in the session after the course unit. Repetition only possible after re-enrolling.
Mode of examination
written 120 minutes
Additional information on mode of examination
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.
Written aids
Four-page handwritten cheat sheet. Electronic aids are not allowed.
This information can be updated until the beginning of the semester; information on the examination timetable is binding.
Learning materials
No public learning materials available.
Only public learning materials are listed.
Groups
No information on groups available.
Restrictions
There are no additional restrictions for the registration.
Performance assessment as a semester course