论文信息 - Two results about the matrix exponential

Two results about the matrix exponential

Abstract Two results about the matrix exponential are given. One characterizes the matrices A which satisfy e A e A H = e A H e A ; another gives upper bounds on trace e A e A H . When A is stable, the bounds preserve the asymptotic stability.

Hongguo Xu | Hongguo Xu

[1] D. Bernstein. Some open problems in matrix theory arising in linear systems and control , 1992 .

[2] J. Snyders,et al. On Nonnegative Solutions of the Equation $AD + DA' = - C$ , 1970 .

[3] Huibert Kwakernaak,et al. Linear Optimal Control Systems , 1972 .

[4] F. R. Gantmakher. The Theory of Matrices , 1984 .

[5] E. Fischer. Über quadratische Formen mit reellen Koeffizienten , 1905 .

[6] Dennis S. Bernstein,et al. Orthogonal Matrices and the Matrix Exponential , 1990, SIAM Rev..

[7] Wasin So. Equality Cases in Matrix Exponential Inequalities , 1992, SIAM J. Matrix Anal. Appl..

[8] C. Loan,et al. Nineteen Dubious Ways to Compute the Exponential of a Matrix , 1978 .

[9] F. Uhlig,et al. On the Matrix Equation f(X) = A , 1992 .

[10] Charles R. Johnson,et al. Topics in Matrix Analysis , 1991 .

[11] Gene H. Golub,et al. Matrix computations , 1983 .

[12] Henryk Minc,et al. On the Matrix Equation X′X = A , 1962, Proceedings of the Edinburgh Mathematical Society.

[13] W. Wonham. Linear Multivariable Control: A Geometric Approach , 1974 .

[14] Peter Lancaster,et al. The theory of matrices , 1969 .

[15] G. Hewer,et al. The sensitivity of the stable Lyapunov equation , 1987, 26th IEEE Conference on Decision and Control.