论文信息 - On bounds of the Riccati and Lyapunov matrix equations

On bounds of the Riccati and Lyapunov matrix equations

Various bounds for the traces of the solutions of the algebraic Riccati and Lyapunov matrix equations are established in the continuous and discrete domain, respectively. The presented results give lower bounds for the sum of the eigenvalue of the matrix solutions.

[1] T. Mori,et al. On the discrete Lyapunov matrix equation , 1982 .

[2] M. Youn,et al. Comments on ‘A note on the discrete Lyapunov and Riccati matrix equations’ , 1985 .

[3] S. Bialas. On the Lyapunov matrix equation , 1980 .

[4] Mitsuhiko Toda,et al. Performance Bounds for Continuous-time Filters in the Presence of Modeling Errors , 1978, IEEE Transactions on Aerospace and Electronic Systems.

[5] K. Hirai,et al. Upper and lower bounds on the solution of the algebraic Riccati equation , 1979 .

[6] V. Karanam. Lower bounds on the solution of Lyapunov matrix and algebraic Riccati equations , 1981 .

[7] T. Mori,et al. A brief summary of the bounds on the solution of the algebraic matrix equations in control theory , 1984 .

[8] M. Toda,et al. Bounds on estimation errors of discrete-time filters under modeling uncertainty , 1978, 1978 IEEE Conference on Decision and Control including the 17th Symposium on Adaptive Processes.

[9] M. Athans,et al. The design of suboptimal linear time-varying systems , 1968 .

[10] M. T. Tran,et al. A note on the discrete Lyapunov and Riccati matrix equations , 1984 .

[11] M. Toda,et al. On norm bounds for algebraic Riccati and Lyapunov equations , 1978 .

[12] Wook Hyun Kwon,et al. A note on the algebraic matrix Riccati equation , 1977 .