(Didier Henrion, LAAS-CNRS, Toulouse, France)

The course focuses on the use of polynomials and polynomial matrices for the analysis and design of linear systems affected by parametric uncertainty.

- 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)

- II.1 - Polytopic uncertainty:
edge theorem (2h30)

II.2 - Multilinear uncertainty: mapping theorem (1h30)

- 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)

- IV.1 - Robust stability analysis:
linear matrix inequalities and
positive polynomial matrices (2h)

IV.2 - Robust stability design: numerical examples (2h)

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The last part contains mostly new (in 2001), previously unpublished material.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.

Last updated on May 23, 2005.