Explicit solution and eigenvalue bounds in the Lyapunov matrix equation
作者： T. Mori , N. Fukuma , M. Kuwahara
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摘要: An explicit solution to the algebraic Lyapunov matrix equation is obtained in terms of controllability pair coefficient matrices. This enables us determine number positive eigenvalues semidefinite through matrix. Based on this formula, upper and lower bounds for each eigenvalue are derived, which always give nontrivial estimates.
sci-hub.se 参考文章(8)
V. Karanam, Lower bounds on the solution of Lyapunov matrix and algebraic Riccati equations IEEE Transactions on Automatic Control. ,vol. 26, pp. 1288- 1290 ,(1981) , 10.1109/TAC.1981.1102803
Per Hagander, Numerical solution of ATS + SA + Q = 0☆ Information Sciences. ,vol. 4, pp. 35- 50 ,(1972) , 10.1016/0020-0255(72)90003-5
N. J. YOUNG, Formulae for the solution of Lyapunov matrix equations International Journal of Control. ,vol. 31, pp. 159- 179 ,(1980) , 10.1080/00207178008961035
V. Karanam, A note on eigenvalue bounds in algebraic Riccati equation IEEE Transactions on Automatic Control. ,vol. 28, pp. 109- 111 ,(1983) , 10.1109/TAC.1983.1103123
I. S. PACE, S. BARNETT, Comparison of numerical methods for solving Liapunov matrix equations International Journal of Control. ,vol. 15, pp. 907- 915 ,(1972) , 10.1080/00207177208932205
E. Shapiro, On the Lyapunov matrix equation IEEE Transactions on Automatic Control. ,vol. 19, pp. 594- 596 ,(1974) , 10.1109/TAC.1974.1100682
K. Yasuda, K. Hirai, Upper and lower bounds on the solution of the algebraic Riccati equation IEEE Transactions on Automatic Control. ,vol. 24, pp. 483- 487 ,(1979) , 10.1109/TAC.1979.1102075
J. Jones, Charles Lew, Solutions of the Lyapunov matrix equation BX - XA = C IEEE Transactions on Automatic Control. ,vol. 27, pp. 464- 466 ,(1982) , 10.1109/TAC.1982.1102902