Algebraic solvability tests for linear matrix inequalities

Author

Scherer, Carsten W.

Author_Institution

Math. Inst., Wurzburg, Germany

fYear

1993

fDate

15-17 Dec 1993

Firstpage

349

Abstract

Discusses algebraic tests for the solvability of the indefinite linear matrix inequality (LMI) (A*P+PA+Q/B*P+S* PB+S/R)⩾0 which arises in the general LQ problem and in H_∞-control. The author presents a new geometric algorithm which allows one to directly reduce the LMI to a certain algebraic Riccati inequality (ARI). Under a mild regularity assumption the author describes how to further reduce the Riccati inequality to an indefinite Lyapunov inequality with a matrix whose eigenvalues are located at the imaginary axis. Finally, the author derives new general necessary conditions for the solvability of such Lyapunov inequalities and discusses cases under which these conditions are also sufficient

Keywords

eigenvalues and eigenfunctions; matrix algebra; optimal control; H_∞ control; LQ problem; algebraic Riccati inequality; algebraic solvability tests; eigenvalues; general necessary conditions; geometric algorithm; indefinite linear matrix inequality; linear matrix inequalities; mild regularity assumption; sufficient conditions; Ear; Eigenvalues and eigenfunctions; Lead; Linear matrix inequalities; Reliability theory; Riccati equations; Stability; Testing;

fLanguage

English

Publisher

ieee

Conference_Titel

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

Conference_Location

San Antonio, TX

Print_ISBN

0-7803-1298-8

Type

conf

DOI

10.1109/CDC.1993.325133

Filename

325133