The rank one mixed μ problem and "Kharitonov-type" methods

Author

Young, Peter M.

Author_Institution

Dept. of Electr. Eng., California Inst. of Technol., Pasadena, CA, USA

fYear

1993

fDate

15-17 Dec 1993

Firstpage

523

Abstract

The general mixed μ problem has been shown to be NP hard, so that the exact solution of the general problem is computationally intractable, except for small problems. In this paper we consider not the general problem, but a particular special case of this problem-the rank one mixed μ problem. We show that for this case the mixed μ problem is equivalent to its upper bound (which is convex), and it can be computed easily (and exactly). This special case is shown to be equivalent to the so called "affine parameter variation" problem (for a polynomial with perturbed coefficients) which has been examined in detail in the literature, and for which several celebrated "Kharitonov-type" results have been proven.

Keywords

eigenvalues and eigenfunctions; matrix algebra; minimisation; polynomials; stability criteria; Kharitonov type methods; affine parameter variation problem; complex matrix; convex minimisation; eigenvalues; parametric uncertainty; polynomial; rank one mixed μ problem; robust stability; upper bound; Eigenvalues and eigenfunctions; Polynomials; Robust stability; Testing; Uncertainty; Upper bound;

fLanguage

English

Publisher

ieee

Conference_Titel

Decision and Control, 1993., Proceedings of the 32nd IEEE Conference on

Print_ISBN

0-7803-1298-8

Type

conf

DOI

10.1109/CDC.1993.325092

Filename

325092