Title :
The rank one mixed μ problem and "Kharitonov-type" methods
Author_Institution :
Dept. of Electr. Eng., California Inst. of Technol., Pasadena, CA, USA
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;
Conference_Titel :
Decision and Control, 1993., Proceedings of the 32nd IEEE Conference on
Print_ISBN :
0-7803-1298-8
DOI :
10.1109/CDC.1993.325092
