ECE685 Introduction to Robust Control

Fall 2005

Course Information

  • Instructor:  Sarah Koskie

  • Email:

  • Lectures:   MW 5:45–7 pm in SL 165 or SL 174

  • Office Hours:   MW 7–8:30 pm in SL 164F or by appointment

  • Textbook: A Course in Robust Control Theory: A Convex Approach by Geir E. Dullerud and Fernando Paganini. Springer, 2000. ISBN: 0-387-98945-5.

    *** Note to students: The notation in this text is very mathematical but the explanations are excellent. Please do not let the notation alarm you. I will explain it in class. The alternative texts listed below use simpler notation but give very little explanation.

  • Suggested references:

  • Prerequisites: ECE602, or consent of instructor. (Topics required: finite-dimensional linear algebra, exposure to control and system theory, and basic concepts from functional analysis.)

  • Objectives: Students will become familiar with the basic concepts and methods of robust control and be able to apply them appropriately to the analysis and design of control systems.

  • Course requirements/exams
    • Occasional homework assignments, which may involve some simple Matlab programming
    • One take-home midterm exam
    • One take-home final exam
  • Students are allowed, even encouraged, to work on the homework in small groups, but each student must write up his or her own homework to hand in.

  • Grading:  
    • homework 34%
    • midterm 33%
    • final exam 33%

Course description

One of the most useful qualities of a properly designed feedback control system is robustness, i.e., the ability of the closed-loop system to continue performing satisfactorily despite large variations in the (open-loop) plant dynamics. This course will provide an introduction to the analysis and design of robust feedback control systems. Topics covered: modeling and paradigms for robust control; robust stability and measures of robust performance; analysis of robust stability and performance; design for robust stability and performance.

Course outline

Robust control -- motivation and overview

Why robust control?
Examples of important robust control problems

Paradigms for robust control

Sources of uncertainties
Parametric families of polynomials or matrices
Multi-model and polytopic systems
Systems with feedback perturbations: Linear fractional transformations; structured perturbations

Measures of robustness

Robust stability; quadratic stability; stability margins; invariant ellipsoids; decay rate
Reachable sets with input constraints
Output energy and peak
H2 and H performance

Computation of robustness measures

Complexity issues
Exact methods for parametric families: Kharitonov and Edge theorems
Polytopic systems: LMI methods
Systems with feedback uncertainties: Small-gain and passivity methods
Systems with structured uncertainties: μ, Km and LMI analysis

Robust synthesis

Polytopic systems: LMI methods
Systems with feedback uncertainties
Systems with structured uncertainties
Gain-scheduled control


Where appropriate, journal papers may be referenced. In addition to the references listed above, the instructor has consulted the following texts which are out of print.
  • New Tools for Robustness of Linear Systems, B.R. Barmish, MacMillan, 1994.
  • Linear Robust Control, M. Green and D.J.N. Limebeer, Prentice Hall, 1995.

Last modified May 15,2007.