LMIs in Control (3V/1U)

Lecturer

Dr. sc. techn. Eric Bullinger

Pfaffenwaldring 9, Zi. 2.245

685 7752

bullinger@ist.uni-stuttgart.de

Time and place (3h lecture + 1h exercise)

Mi. 11.30-13.00, V 9.31		Starting October 22nd, 2003
Fr. 11.30-13.00, V 9.22

Course description

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.

Outline

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
  • stability
  • robustness
• 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 equivalent lectures.

The course will be given in English.

Literature

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 Sons 1999.
• Antoulas, A.C., Sorensen, D.C. and Gugercin, S.: A survey of model reduction methods for large-scale systems, Technical Report Rice University, 1999.