Course on polynomial methods for robust control
(Didier Henrion, LAAS-CNRS, Toulouse, France)

Universidad de los Andes, Merida, Venezuela - October and November 2001

Description

Outline and slides

• Monday October 29, 2001 - Robust stability analysis Part I
  I.0 - General introduction: linear systems, polynomial methods and robust control (1h)
  I.1 - Single parameter uncertainty: eigenvalue criteria (1h30)
  I.2 - Interval uncertainty: Kharitonov's theorem (1h30)
  
• Tuesday October 30, 2001 - Robust stability analysis Part II
  II.1 - Polytopic uncertainty: edge theorem (2h30)
  II.2 - Multilinear uncertainty: mapping theorem (1h30)
  
• Wednesday October 31, 2001 - Robust design and convex optimization
  III.1 - Robust pole placement: approximation of stability region (1h30)
  III.2 - Robust stabilization: Youla-Kucera and Rantzer-Megretski parametrizations (1h30)
  III.3 - Simultaneous stabilization: strong stabilization, Hermite criterion, open problems (1h)
  
• Thursday November 1, 2001 - New results on robust analysis and design
  IV.1 - Robust stability analysis: linear matrix inequalities and positive polynomial matrices (2h)
  IV.2 - Robust stability design: numerical examples (2h)
  

  Material

  Most of the material of the first two parts is taken from the textbooks [J. Ackermann. Robust control: systems with uncertain physical parameters. Springer, 1993], [B. R. Barmish. New tools for robustness of linear systems. MacMillan, 1994] and [S. P. Bhattacharyya, H. Chapellat, L. H. Keel. Robust control - The parametric approach. Prentice Hall, 1995].
  The third part describes relatively recent results published from 1992 to 1999.
  The last part contains mostly new (in 2001), previously unpublished material.

  Computations for the illustrative examples described throughout the course were carried out with the commercial software [H. Kwakernaak, M. Sebek. The Polynomial Toolbox for Matlab. PolyX Ltd, 1998.]

  Other courses on polynomial methods can be downloaded from PolyX home page.

  Acknowledgments

  Thanks to Michael Sebek, Zdenek Hurak (Czech Technical University in Prague) and Jean-Pierre Merlet (INRIA Sophia-Antipolis) for pointing out several errors in the slides.

  Last updated on October 10, 2002.