Title :
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
fDate :
12/1/1994 12:00:00 AM
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;
Journal_Title :
Automatic Control, IEEE Transactions on
