Closed form solutions for a class of LMIs

Author

Parrilo, Pablo A. ; Khatri, Sven

Author_Institution

California Inst. of Technol., Pasadena, CA, USA

Volume

1

fYear

1998

fDate

21-26 Jun 1998

Firstpage

87

Abstract

An exact solution for a special class of cone-preserving linear matrix inequalities (LMIs) is developed. By using a generalized version of the classical Perron-Frobenius theorem, the optimal value is shown to be equal to the spectral radius of an associated linear operator. This allows for a much more efficient computation of the optimal solution, using for instance power iteration-type algorithms. This particular LMI class appears in the computation of upper bounds for some generalizations of the structured singular value μ (spherical μ). Examples and comparisons with previous techniques are provided

Keywords

eigenvalues and eigenfunctions; matrix algebra; LMIs; classical Perron-Frobenius theorem; closed form solutions; cone-preserving linear matrix inequalities; linear operator; power iteration-type algorithms; spectral radius; structured singular value; upper bounds; Computational efficiency; Control systems; Control theory; Linear matrix inequalities; Polynomials; Riccati equations; Solids; Upper bound;

fLanguage

English

Publisher

ieee

Conference_Titel

American Control Conference, 1998. Proceedings of the 1998

Conference_Location

Philadelphia, PA

ISSN

0743-1619

Print_ISBN

0-7803-4530-4

Type

conf

DOI

10.1109/ACC.1998.698577

Filename

698577