LMIs in Control (3V/1U)
- Time and place (3h lecture + 1h exercise)
winter terms: 2000/01, 2001/02, and 2002/03
Practical controller design problems usually require
achieving several objectives simultaneously: limit the effect of
disturbances like measurement noise, keep the input signal within bounds,
minimize an objective function (i.e.\ LQR), etc.
For linear systems, such multi-objective designs can efficiently be
solved with Linear Matrix Inequalities (LMIs). We will first precisely
define different control objectives, then see how to cast analysis
and controller design problems into LMIs, and finally solve the LMIs with computers.
Most analysis and controller synthesis tools are applicable only for
small systems. The second part of the course therefore deals with the
problem of model reduction for large-scale linear system, resulting in
models usable for analysis and controller design.
The lecture is supplemented by classroom and computer exercises.
Some of the topics to be covered include:
- linear systems, signal spaces, norms
- Lyapunov-, Riccatti-, Sylvester equations in control
- passivity and dissipativity
- basics on LMIs
- system analysis using LMIs
- controller synthesis in the framework of LMIs
- H_infinity design
- H2 design
- positive real design
- multi-objective design
- nominal and robust design
- LPV/gain scheduling
- model reduction techniques
- SVD based methods
- moment matching (Lanzcos, Arnoldi, ...)
The course is intended to students having attended RT I and RT II or
The course will be given in English.
The course is based on the following books and articles
- Zhou, K., Doyle, J. C. and Glover, K.: Robust and Optimal
Control, Prentice Hall, 1996.
- Scherer, C. and Weiland, S.: Lecture Notes DISC Course on
Linear Matrix Inequalities in Control, 2000.
- Boyd, S., El Ghaoui, L., Feron, E. and Balakrishnan, V.:
Linear Matrix Inequalities in System and Control Theory, SIAM 1994.
- El Ghaoui, Niculescu, S.-I.: Advances in Linear Matrix
Inequality Methods in Control, Siam 1999.
- Antoulas, A.C.: Approximation of linear dynamical systems,
Encyclopedia of Electrical and Electronics Engineering, Wiley and
- Antoulas, A.C., Sorensen, D.C. and Gugercin, S.: A survey of
model reduction methods for large-scale systems, Technical Report
Rice University, 1999.