Matrix rank-robustness problems in systems and control: Theory and computation

Mark Alan Wicks, Purdue University

Abstract

This thesis investigates the theory and computation of several measures of the rank robustness of general system matrices with respect to structured parameter variations. More specifically, it investigates the problem of locating a minimum norm matrix perturbation that lies in some specified set and causes some prespecified rectangular matrix to lose rank. It also investigates the problem of finding the magnitude of perturbations which cause a given matrix pencil to fail to have full rank. As many system properties are characterized by either a rank test, or the rank of a matrix pencil, the size of these minimum rank-reducing perturbations quantify the size of parameter variations that can cause some desirable system property to fail to hold. Two specific robustness problems are investigated in detail: the problem of locating the smallest real or complex matrix perturbation which renders a system uncontrollable and the problem of locating the smallest real matrix perturbation that causes a complex rectangular matrix to lose rank. The thesis presents numerical algorithms which are shown to converge to local minima of these two problems. The numerical stability and accuracy of these algorithms is examined. After studying these problems, the thesis proposes a framework for solving more general matrix rank-robustness problems. Numerical algorithms for the general problems are presented. The thesis studies the convergence and accuracy of these algorithms.

Degree

Ph.D.

Advisors

DeCarlo, Purdue University.

Subject Area

Electrical engineering

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