Iterative solutions to the Kalman-Yakubovich-conjugate matrix equation

Applied Mathematics and Computation

Volumn 217, Issue 9, 2011, Pages 4427-4438

  Wu, Ai Guo ^a   Feng, Gang ^b   Duan, Guang Ren ^a   Liu, Wanquan ^c  

^a HARBIN INSTITUTE OF TECHNOLOGY   (China)

^b CITY UNIVERSITY OF HONG KONG   (Hong Kong)

^c CURTIN UNIVERSITY   (Australia)

Author keywords

Convergence order; Kalman Yakubovich conjugate matrix equation; Smith iteration

Indexed keywords

COMPLEX MATRICES; CONVERGENCE ORDER; CONVERGENCE PROPERTIES; EXPLICIT SOLUTIONS; INFINITE SERIES; ITERATIVE ALGORITHM; ITERATIVE SOLUTIONS; KALMAN-YAKUBOVICH-CONJUGATE MATRIX EQUATION; MATRIX EQUATIONS; SMITH ITERATION;

ALGORITHMS; ITERATIVE METHODS; MATRIX ALGEBRA;

CONVERGENCE OF NUMERICAL METHODS;

EID: 78650171410     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2010.10.041     Document Type: Article

References (25)

1. R.R. Bitmead Explicit solutions of the discrete-time Lyapunov matrix equation and Kalman-Yabovich equations IEEE Transactions on Automatic Control AC-26 6 1981 1291 1294
2. L. Huang The extension of Roth's theorem for matrix equation over a ring Linear Algebra and Its Application 259 1997 229 235
3. R.R. Bitmead, and H. Weiss One the solution of the discrete-time Lyapunov matrix in controllable canonical form IEEE Transactions on Automatic Control AC-24 3 1979 481 482
4. B. Hanzon A Faddeev sequence method for solving Lyapunov and Sylvester equations Linear Algebra and Its Applications 241-243 1996 401 430
5. B. Zhou, and G.R. Duan Parametric solutions to the generalized discrete Sylvester matrix equation MXN - X = TY and their applications IMA Journal of Mathematical Control and Information 26 2009 59 78
6. T. Jiang, and M. Wei On solutions of the matrix equations X - AXB = C and X - A X B = C Linear Algebra and Its Application 367 2003 225 233
7. A.G. Wu, H.Q. Wang, and G.R. Duan On matrix equations X - AXF = C and X - A X F = C Journal of Computational and Applied Mathematics 2009 10.1016/j.cam.2009.01.013
8. T + B = 0 IEEE Transactions on Automatic Control 16 3 1971 278 279
9. T. Mom, N. Fukuma, and M. Kuwahara Eigenvalue bounds for the discrete Lyapunov matrix equation IEEE Transactions on Automatic Control AC-30 9 1985 925 926
10. F. Ding, and T. Chen On iterative solutions of general coupled matrix equations SIAM Journal on Control Optimization 44 6 2006 2269 2284
11. P. Benner, E.S. Quintana-Qrti, and G. Quintana-Qrti Solving stable Stein equations on distributed memory computers Lecture Notes in Computer Science 1685 1999 1120 1123
12. R.A. Smith Matrix equation XA + BX = C SIAM Journal on Applied Mathematics 16 1968 198 201
13. T. Penzl A cyclic low-rank Smith method for large sparse Lyapunov equations SIAM Journal on Scientific Computing 21 4 2000 1401 1418
14. S. Gugercin, D.C. Sorensen, and A.C. Antoulas A modified low-rank Smith method for large-scale Lyapunov equations Numerical Algorithms 32 2003 27 55
15. B. Zhou, J. Lam, and G.R. Duan On Smith-type iterative algorithms for the Stein matrix equation Applied Mathematics Letters 22 2009 1038 1044
16. F. Ding, and T. Chen Iterative least squares solutions of coupled Sylvester matrix equations Systems and Control Letters 54 2 2005 95 107
17. L. Xie, J. Ding, and F. Ding Gradient based iterative solutions for general linear matrix equations Computers and Mathematics with Applications 58 7 2009 1441 1448
18. F. Ding, P.X. Liu, and J. Ding Iterative solutions of the generalized Sylvester matrix equations by using the hierarchical identification principle Applied Mathematics and Computation 197 1 2008 41 50
19. F. Ding, and T. Chen Hierarchical gradient-based identification of multivariable discrete-time systems Automatica 41 2 2005 315 325
20. F. Ding, and T. Chen Hierarchical least squares identification methods for multivariable systems IEEE Transactions on Automatic Control 50 3 2005 397 402
21. A.G. Wu, G.R. Duan, and Y. Xue Kronecker maps and Sylvester-polynomial matrix equations IEEE Transactions on Automatic Control 52 5 2007 905 910
22. A.G. Wu, and G.R. Duan Explicit general solution to the matrix equation AV + BW = EVF + R IET Control Theory and Application 2 1 2008 56 60
23. A.G. Wu, G.R. Duan, and B. Zhou Solution to generalized Sylvester matrix equations IEEE Transactions on Automatic Control 53 3 2008 811 815
24. A.G. Wu, G. Feng, J. Hu, and G.R. Duan Closed-form solutions to the nonhomogeneous Yakubovich-conjugate matrix equation Applied Mathematics and Computation 214 2 2009 442 450
25. A.G. Wu, G. Feng, G.R. Duan, and W.J. Wu Iterative solutions to coupled Sylvester-conjugate matrix equations Computers and Mathematics with Applications 60 1 2010 54 66