ECE 699

SPECIAL TOPICS

Topics in Robust Control:
Simultaneous Stabilization

You can download a .pdf version of the course syllabus.

Class Time: Monday, 7:20 - 10:00 p.m., Aquia Module, Room 104, Dr. Beale

Prerequisite: Grade of B or better in ECE 521

Text: Course notes provided by the Instructor.

Recommended Text: Control System Synthesis: A Factorization Approach, by M. Vidyasagar, MIT Press, 1985, Chapters 1 - 6. This text is out of print. If you plan to do any work in the area of robust control using a factorization approach, it is a book that you should try to find. It is available in both hard and soft cover editions. The ISBN number is 0-262-22027-X.

Objectives:

 To introduce students to the general problem of robust control and to the mathematical basis of simultaneous stabilization.

To develop students' ability to read the literature and to pursue research in robust control, particularly in the area of simultaneous stabilization.

Grading:

Grading will be based on two projects, a paper review, and a final exam. Each of these activities will count 25% of the course grade.

Important Dates:

The final exam will be on Monday, May 10, 7:30--10:15 p.m.

Last Day to Drop without Dean's Permission: Friday, February 20

No classes the week of March 8 due to SPRING BREAK!!!

Project Descriptions:

Design Project #1, Issues in Stability

Design Project #2, Three-Plant Simultaneous Stabilization

Project #3, Paper Review

Course Outline

Introduction, definitions of robust control, form for the standard control problem, performance characteristics and limitations -- 1 class period.
Mathematical preliminaries, rings and fields, Euclidian domains, rings of proper stable transfer functions, coprime factorizations -- 2 class periods.
Internal stability, the problem with unstable pole/zero cancellations, the 2-input/2-output system  -- 1 class period.
Strong stabilization, the parity interlacing property, and its dual property -- 1 class period.
Youla parametrization of all controllers that stabilize a system, closed-loop poles and zeros in terms of the parametrization -- 2 class periods.
Simultaneous stabilization of two systems, the associated system, necessary and sufficient conditions for a solution, interpolation, extension of simultaneous stabilization to three or more systems, auxiliary systems, the loss of sufficient conditions, stable simultaneous stabilization -- 5 class periods.
Additional topics in simultaneous stabilization, multiple bounded domains of stability, the extended parity interlacing property, convex combinations of systems -- 2 class periods.

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Latest revision on 02/08/04 07:39 PM