Welcome to Linear Matrix Inequalities in Control


In the space of the last two decades or so, Linear Matrix Inequalities (LMIs) have become a de facto standard tool in numerical analysis and design in Control Engineering. Many standard problems, such as stability, robustness, performance and state feedback design, are naturally formulated as LMIs. The advantage of formulating a controller design problem with LMIs is that additional constraints can easily be added. As an example, a linear quadratic regulator (lqr) can be designed subject to constraints on the domain of the closed-loop poles. In addition, various efficient numerical toolboxes have been developed over the years, permitting straightforward usage of LMIs in practical settings.

The theory is applied to practical examples to give hands on experience with the theory.


This course highlights a number of different usages of LMIs for solving various control-theoretic problems, covering the following main subjects:

- Convex optimization and toolboxes

- Dissipative systems

- Stability analysis

- Parametric uncertainties

- Feedback design

Prerequisites: Basic linear systems theory as taught on the 8th semester of the Automation & Control education or similar.

Organizer: Associate Professor Jan Bendtsen
Lecturers: Associate Professor Jan Bendtsen, Associate Professor John Leth & Assistant Professor Christoffer Sloth

ECTS: 3.0

Time: 19, 20, 23, 24, 26 and 27 May 2016 09:00-16:00


Zip code: 9220

City: Aalborg 

Number of seats: 40

Deadline: April 10, 2016

Important information concerning PhD courses: We have over some time experienced problems with no-show for both project and general courses. It has now reached a point where we are forced to take action. Therefore, the Doctoral School has decided to introduce a no-show fee of DKK 5,000 for each course where the student does not show up. Cancellations are accepted no later than 2 weeks before start of the course. Registered illness is of course an acceptable reason for not showing up on those days. Furthermore, all courses open for registration approximately three months before start. This can hopefully also provide new students a chance to register for courses during the year. We look forward to your registrations.