Course Objectives

The course will give an introduction to analysis and design of robust multivariable control systems. The focus is on inherent limitations in feedback systems and on stability and performance in the presence of uncertainty. Important topics include: signal and system norms, performance specifications and inherent limitations, uncertainty descriptions,  robust stability and robust performance, structured uncertainty and mu, H_infty- and H_2-optimal control, LQG cast as H_2-optimal control, H_infty loop shaping, mu-synthesis, LMIs, gap metrics.

Intended learning outcomes 

After completing the course, the student should be able to:

• describe and explain the general principles for analysis and synthesis of robust multivariable control systems.
• derive fundamental limitations in feedback systems based on interpolation constraints and analytic constraints on closed-loop transfer-functions
• model uncertainty in linear dynamic systems using model sets
• derive and apply conditions for robust stability and robust performance of multivariable feedback systems with respect to structured and unstructured uncertainty
• quantify the achievable control performance for a given system
• design/synthesize multivariable controllers for robust performance

Prerequisites

Undergraduate course in classic SISO control, elementary background in matrices and linear algebra. An introductory course in multivariable control is recommended, but not a requirement.

Schedule

The course will consist of 8 lectures, with the first lecture starting Tue January 17 2023, 10-12 in Harry Nyquist room, Malvinas v 10. There will be 1-2 lectures per week. The full schedule will be announced later. For each lecture there will be a compulsory exercise with hand in. At the end of the course there will be a take home exam.

Preliminary course outline

See course homepage in Canvas

Course requirements

Active presence at lectures (unless absence permitted)

Reading the assigned chapters in course book before coming to lecture.

Weekly hand-in problems (80% required on each)

24h take-home exam at the end of the course

Course Literature

• Course book:
  Multivariable Feedback Control - Analysis and Design, 2nd ed.
  Sigurd Skogestad and Ian Postlethwaite
  Wiley, 2005
  ISBN 0-470-01168-8 
• Supporting book:
  Essentials of Robust Control
  Kemin Zhou, John C. Doyle
  Prentice Hall, 1998
  ISBN 0135258332

• Handouts

Registration

Please send an email with name and affiliation to Elling W. Jacobsen