Browse > Article

New Unified bounds for the solution of the Lyapunov matrix equation for Decentralized Singularly Perturbed Unified System  

Lee, Dong-Gi (Department of Electronics & Information Engineering, Konyang University)
Oh, Do-Chang (Department of Electronics & Information Engineering, Konyang University)
Publication Information
Journal of the Institute of Electronics Engineers of Korea SC / v.46, no.1, 2009 , pp. 34-42 More about this Journal
Abstract
In this paper, new bounds for the solution of the unified Lyapunov matrix equation for decentralized singularly perturbed systemare obtained, and some of the existing works using deficient assumptions are also generalized.
Keywords
Lyapunov matrix inequalities; unified system; bound estimates; singularly perturbed system;
Citations & Related Records
Times Cited By KSCI : 1  (Citation Analysis)
연도 인용수 순위
1 Y. Feng, K.A. Loparo, and X. Feng, 'New Estimates for Solutions of Lyapunov Equations,' IEEE Trans. on Automatic Control, vol. 42, pp. 408-411, March 1997   DOI   ScienceOn
2 N. Komaroff, 'Upper summation and product bounds for solution eigenvalues of the Lyapunov matrix equation,' IEEE Trans. on Automatic Control, vol. 37, pp. 1040-1042, 1992   DOI   ScienceOn
3 V.R. Karanam, ':Lower bounds on the solution of Lyapunov matrix and algebraic Riccati equations,' IEEE Trans. on Automatic Control, vol. 26, pp. 1288-1290, 1981   DOI
4 T. Mori, N. Fukuma and M. Kuwahara, 'Eigenvalue bounds for the discrete Lyapunov matrix equation,' IEEE Trans. on Automatic Control, vol. 30, pp. 925-926, 1985   DOI
5 R.H. Middleton and G.C. Goodwin, Digital Control and Estimation: A Unified approach. Prentice-Hall, Englewood Cliffs, NJ, 1990
6 M.T. Tran and M.E. Sawan, 'A note on the discrete Lyapunov and Riccati matrix equations,' International Journal of Control, vol. 23, pp. 87-88, 1978
7 W.H. Kwon, M.J. Youn and Z. Bien, 'On bounds of the Riccati and Lyapunov matrix equation,' IEEE Trans. on Automatic Control, vol. 30, pp. 1134-1135, 1985   DOI
8 T. Mori, N. Fukuma and M. Kuwahara, 'On the discrete Lyapunov matrix equation,' IEEE Trans. on Automatic Control, vol. 27, pp. 463-464, 1982   DOI
9 M. Mrabti and A. Hmamed, 'Bounds for the solution of the Lyapunov matrix equation-A unified approach,' Syst. Contr. Lett., vol. 18, pp. 73-81, 1992   DOI   ScienceOn
10 R.V. Patel and M. Toda, 'On norm bounds for algebraic Riccati and Lyapunov equation,' IEEE Trans. on Automatic Control, vol. 23, pp. 87-88, 1978   DOI
11 N. Komaroff, 'Upper bounds for the eigenvalues of the solution of the discrete Lyapunov matrix equation,' IEEE Trans. on Automatic Control, vol. 35, pp. 468-469, 1990   DOI   ScienceOn
12 Chien-Hua Lee, 'Upper and lower matrix bounds of the solution for the discrete Lyapunov equation,' IEEE Trans. on Automatic Control, vol. 41, pp. 1338-1341, 1996   DOI   ScienceOn
13 N. Komaroff, 'Upper bounds for the eigenvalues of the solution of the Lyapunov matrix equation,' IEEE Trans. on Automatic Control, vol. 35, pp. 737-739, 1990   DOI   ScienceOn
14 N. Komaroff, 'Simultaneous eigenvalue lower bounds for the Lyapunov matrix equation,' IEEE Trans. on Automatic Control, vol. 33, pp. 126-128, 1988   DOI   ScienceOn
15 N. Komaroff and B. Shahian, 'Lower summation bounds for the solution of the discrete Riccati and Lyapunov equation,' IEEE Trans. on Automatic Control, vol. 37, pp. 1078-1080, 1992   DOI   ScienceOn
16 K. Yasuda and K. Hirai, 'Upper and lower bounds on the solution of the algebraic Riccati equation,' IEEE Trans. on Automatic Control, vol. 24, pp. 483-487, 1979   DOI
17 N. Komaroff, 'Lower bounds for the solution of the discrete algebraic Lyapunov equation,' IEEE Trans. on Automatic Control, vol. 37, pp. 1017-1018, 1992   DOI   ScienceOn
18 J. Garloff, 'Bounds for the eigenvalues of the solution of the discrete Riccati and Lyapunov equation and the continuous Lyapunov equation,' International Journal of Control, vol. 43, pp. 423-431, 1986   DOI   ScienceOn
19 T. Mori, N. Fukuma and M. Kuwahara, 'On the discrete Riccati equation,' IEEE Trans. on Automatic Control, vol. 32, pp. 828-829, 1987   DOI
20 D. Lee, G. Heo, and J. Woo, 'New Bounds using the solutionof the Discrete Lyapunov Matrix Equation,', International Journal of Control, Automation, and Systems, vol. 1, pp. 459-463, 2003   ScienceOn
21 T. Mori, 'On some bounds in the algebraic Riccati and Lyapunov equations,' IEEE Trans. on Automatic Control, vol. 30, pp. 162-164, 1985   DOI   ScienceOn
22 I. Hyun, M. Sawan, D. Lee, and D. Kim, 'Robust Stability for Decentralized Singularly Perturbed Unified System,' Proceedings of the 2006 American Control Conference, pp. 4338-4343, 2006   DOI
23 Hardev Singh, 'Unified Approach for Singularly Perturbed Control Systems,' Ph.D. dissertation, Marquette University, Wichita, May 2001
24 T. Mori, N. Fukuma, and M. Kuwahara, 'Bounds in the Lyapunov matrix differential equation,' IEEE Trans. on Automatic Control, vol. 32, no. 1, pp. 55-57, March 1987   DOI
25 M. Mrabti and A. Hmamed, 'Unified type algebraic Lyapunov matrix equation: simultaneous eigenvalue bounds,' Adv. Modeling & Analysis, AMSE Press, vol. 12, pp. 57-63, 1992
26 T. Mori, I.A. Derese, 'A brief summary of the bounds on the solution of the algebraic matrix equations in control theory,' International Journal of Control, vol. 39, pp. 247-256, 1984   DOI   ScienceOn
27 Y. Feng, K.A. Loparo, and X. Feng, 'Inequalities for the trace of matrix product,' IEEE Trans. on Automatic Control, vol. 39, pp. 2489-2490, December 1994   DOI   ScienceOn