# INFT 940

## SPECIAL TOPICS IN CONTROL THEORY

## Topics in Robust Control

Polynomial Approach to Stability Analysis

**Schedule:** Spring '97, Thursday, 7:20 - 10:00 p.m., S&T II, Room
128, Dr. Beale
**Prerequisite:** ECE 521 or POI.

**Text:** *New Tools for Robustness in Linear Systems*, B.R.
Barmish, Macmillan, 1994, Chapters 1 - 11.

**Objectives:** To investigate some of the most recent tools which have
been developed for the analysis of stability robustness in linear systems
and to see how these tools might be extended to the synthesis of
controllers.

Project #1

Project #2

Paper Review

You may download the MATLAB.m files that were
written for these examples. After you download the file, you must unzip it to re-generate the .m files. No guarantee is given for these routines.

**Course Outline, Spring '97:**

` `
Chapter 1 -- Introduction to robust control, comparison of the polynomial
approach with other methods, such as LQG/LTR, H_infinity, and simultaneous
stabilization, value sets and zero exclusion -- 1 class period.

` `
Chapter 2 -- Types of uncertainty structures, simple examples of uncertainty,
notation for uncertainty and uncertain families -- 1 class period.

` `
Chapter 3 -- Case study: the system model, uncertainty in the model,
controller structure, the characteristic equation -- 1/2 class period.

` `
Chapter 4 -- Systems with a single uncertain parameter, root locus and
Nyquist methods for graphical analysis of robustness, the eigenvalue
criteria, robust stability for domains -- 2 class periods.

` `
Chapter 5 -- Interval polynomial families, testing sets, Kharitonov
polynomials and rectangles, zero exclusion, robustness margins, graphical
tests -- 2 class periods.

` `
Chapter 6 -- Kharitonov polynomials for low-order systems, interval plants,
robustness margin, the Tsypkin-Polyak function, Tsypkin-Polyak plots --
1 class period.

` `
Chapter 7 -- Value sets, more on the zero exclusion principle,
D-stability -- 1 class period.

` `
Chapter 8 -- Affine linear uncertainty structure, convex hulls, polytopes,
value sets which are polygons, comparison with independent uncertainty --
2 class periods.

` `
Chapter 9 -- Extreme point results, the Edge Theorem, case study
re-visited --2 class periods.

` `
Chapter 10 -- Interval plant with a fixed compensator, operations on
Kharitonov rectangles, octagonal value sets, the 32 Edge Theorem --
1.5 class periods.

` `
Chapter 11 -- Interval plant with low-order compensator, the 16 Plant
Theorem, compensator synthesis -- 1 class period.

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*Latest revision on 05/08/01 08:47 PM
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