Graduate School in Systems and Control

2003 - 2004

ANALYSIS OF FEEDBACK SYSTEMS :
THEORY AND COMPUTATION

Lecturers :
U. Jönsson (Royal Institute of Technology, Sweden),
R. Sepulchre (Ulg),
J.-C. Willems (KULeuven)

• Information
• Slides of lectures
• Reading material
• Evaluation
  

• The aim of the course is to cover the main developments of the theory of feedback systems within the unifying framework of Integral Quadratic Constraints. The emphasis of the course will be on the cross-fertilization of input-output and state-space approaches in the development of the theory. The course will also emphasize how the theory has led to computationally tractable stability criteria for systems that include multivariable components, nonlinearities, and time-varying uncertainties.
  The course will be accessible to engineers and mathematicians with basic background in nonlinear systems, Lyapunov stability, and input-output stability.

  Dates : February 2 - 5 - 9 -12 - 16- 19, 2004

  Schedule : 9h15 -12h30

  This course will take place at CESAME, Bâtiment Euler, 4, av. G. Lemaître, 1348 Louvain-la-Neuve
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• Lecture 1: From absolute stability to Integral Quadratic Constraints. (R. Sepulchre) (ps/pdf).

• Lecture 2: Analysis of feedback systems. The input-output approach (R. Sepulchre)  (ps/pdf).

• Lecture 3 : Dissipativity  theory (J.C. Willems)  (ps/pdf).

• Lecture 4: More on dissipativity: interconnections and positive realness  (J.C. Willems) (ps/pdf).

• Lecture 5: Integral Quadratic Constraints (U. Jonsson) ( part I (ps/pdf); part II (ps/pdf) )

• Lecture 6: Integral Quadratic Constraints: optimization and computations (U. Jonsson)   (ps/pdf).

• Lecture notes on Integral Quadratic Constraints (U. Jonsson)

• J.C. Willems Dissipative dynamical systems - Part I: General theory
  Archive for Rational Mechanics and Analysis
  Volume 45, pages 321-351, 1972.
• J.C. Willems Dissipative dynamical systems - Part II: Linear systems with quadratic supply rates
  Archive for Rational Mechanics and Analysis
  Volume 45, pages 352-393, 1972.
• J.C. Willems Least squares stationary optimal control and the algebraic Riccati equation
  IEEE Transactions on Automatic Control
  Volume 16, pages 621-634, 1971.
• C-Y Kao, A. Megretski, U. Jonsson, A. Rantzer A MATLAB toolbox for Robustness Analysis (Preprint)

• A. Megretski and A. Rantzer. System Analysis via Integral Quadratic Constraints
IEEE Transactions on Automatic Control, 47:6, pp. 819-830, 0 1997
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• Homework 1 (pdf) to be sent to Rodolphe Sepulchre  by March 1
• Homework 2 (pdf) to be sent to Jan Willems by March 1
• Homework 3 (pdf) to be sent to Ulf Jönsson  by March 1