Convexity property of the one-sided multivariable stability margin

Author

Tekawy, Jonathan A. ; Safonov, Michael G. ; Chiang, Richard Y.

Author_Institution

Northrop Corp., Hawthorne, CA, USA

Volume

37

Issue

4

fYear

1992

fDate

4/1/1992 12:00:00 AM

Firstpage

496

Lastpage

498

Abstract

In evaluating the stability robustness of multivariable control systems having one-sided parameter uncertainty, a problem that naturally arises is the minimization over diagonal matrices D of the greatest eigenvalue of (e/sup D/Ae/sup -D/+(e/sup D/Ae/sup -D/)*)/2. The minimization is proved to be convex, thus guaranteeing that every local minimum is also a global minimum and, in theory, guaranteeing the global convergence of generalized gradient nonlinear programming algorithms for computing the minimizing D.<>

Keywords

convergence; eigenvalues and eigenfunctions; linear programming; matrix algebra; minimisation; multivariable control systems; stability; diagonal matrices; generalized gradient nonlinear programming algorithms; global convergence; global minimum; greatest eigenvalue; local minimum; minimization; multivariable control systems; one-sided multivariable stability margin; one-sided parameter uncertainty; stability robustness; Automatic control; Computer aided manufacturing; Control systems; Flexible manufacturing systems; Job shop scheduling; Processor scheduling; Pulp manufacturing; Real time systems; Robust stability; Virtual manufacturing;

fLanguage

English

Journal_Title

Automatic Control, IEEE Transactions on

Publisher

ieee

ISSN

0018-9286

Type

jour

DOI

10.1109/9.126584

Filename

126584