Inequalities for the trace of matrix product

Author

Fang, Yuguang ; Loparo, Kenneth A. ; Feng, Xiangbo

Author_Institution

Dept. of Syst. Eng., Case Western Reserve Univ., Cleveland, OH, USA

Volume

39

Issue

12

fYear

1994

fDate

12/1/1994 12:00:00 AM

Firstpage

2489

Lastpage

2490

Abstract

To obtain estimates of solutions of Lyapunov and Riccati equations which frequently occur in the stability analysis and optimal control design in linear control theory, many researchers have attempted to determine upper and lower bounds for the product of two matrices in terms of the trace of one matrix and the eigenvalues of the other. Baksalary and Puntanen claimed (“An inequality for the trace of matrix product”, ibid., vol. 37, no. 2, p. 239-40, 1992) that they had obtained a better estimate for the trace of the product of two matrices. The purpose of this note is to point out that their main result is incorrect and a counterexample is presented

Keywords

Lyapunov matrix equations; Riccati equations; control system analysis; control system synthesis; optimal control; stability; Lyapunov equations; Riccati equations; linear control theory; lower bounds; matrix product trace inequalities; optimal control design; stability analysis; upper bounds; Control systems; Eigenvalues and eigenfunctions; Linear matrix inequalities; Matrix decomposition; Symmetric matrices; Systems engineering and theory;

fLanguage

English

Journal_Title

Automatic Control, IEEE Transactions on

Publisher

ieee

ISSN

0018-9286

Type

jour

DOI

10.1109/9.362841

Filename

362841