Iterative solutions of the generalized Sylvester matrix equations by using the hierarchical identification principle

Applied Mathematics and Computation

Volumn 197, Issue 1, 2008, Pages 41-50

  Ding, Feng ^a   Liu, Peter X ^b   Ding, Jie ^a  

^a JIANGNAN UNIVERSITY   (China)

^b CARLETON UNIVERSITY   (Canada)

Author keywords

Gauss Seidel iteration; Gradient search principle; Hierarchical identification principle; Jacobi iteration; Matrix equations

Indexed keywords

HIERARCHICAL SYSTEMS; ITERATIVE METHODS; LEAST SQUARES APPROXIMATIONS; NONLINEAR EQUATIONS; PROBLEM SOLVING;

GAUSS-SEIDEL ITERATION; GRADIENT SEARCH PRINCIPLE; HIERARCHICAL IDENTIFICATION PRINCIPLES; JACOBI ITERATION; MATRIX EQUATIONS;

MATRIX ALGEBRA;

EID: 38949156204     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2007.07.040     Document Type: Article

References (22)

1. Golub G.H., and Van Loan C.F. Matrix Computations. 3rd ed. (1996), Johns Hopkins University Press, Baltimore, MD
2. Ding F., and Chen T. On iterative solutions of general coupled matrix equations. SIAM Journal on Control and Optimization 44 6 (2006) 2269-2284
3. Ding F., and Chen T. Iterative least squares solutions of coupled Sylvester matrix equations. Systems & Control Letters 54 2 (2005) 95-107
4. Ding F., and Chen T. Gradient based iterative algorithms for solving a class of matrix equations. IEEE Transactions on Automatic Control 50 8 (2005) 1216-1221
5. F. Ding, M. Li, J.Y. Dai, Hierarchical identification principle and a family of iterative methods, in: Proceedings of the 25th Chinese Control Conference, August 7-11, 2006, Harbin, Heilongjiang, PR China, pp. 418-422.
6. Ljung L. System Identification: Theory for the User. 2nd ed. (1999), Prentice-Hall, Englewood Cliffs, NJ
7. Ding F., and Chen T. Hierarchical gradient-based identification of multivariable discrete-time systems. Automatica 41 2 (2005) 315-325
8. Ding F., and Chen T. Hierarchical least squares identification methods for multivariable systems. IEEE Transactions on Automatic Control 50 3 (2005) 397-402
9. Ding F., Liu P.X., and Shi Y. Convergence analysis of estimation algorithms of dual-rate stochastic systems. Applied Mathematics and Computation 176 1 (2006) 245-261
10. Ding F., and Xiao Y.S. A finite-data-window least squares algorithm with a forgetting factor for dynamical modeling. Applied Mathematics and Computation 186 1 (2007) 184-192
11. Ding F., Chen H.B., and Li M. Multi-innovation least squares identification methods based on the auxiliary model for MISO systems. Applied Mathematics and Computation 187 2 (2007) 658-668
12. Ding F., and Chen T. Identification of Hammerstein nonlinear ARMAX systems. Automatica 41 9 (2005) 1479-1489
13. Ding F., Shi Y., and Chen T. Performance analysis of estimation algorithms of non-stationary ARMA processes. IEEE Transactions on Signal Processing 54 3 (2006) 1041-1053
14. Ding F., and Chen T. A gradient based adaptive control algorithm for dual-rate systems. Asian Journal of Control 8 4 (2006) 314-323
15. Ding F., Chen X.W., and Wang J.H. Performance analysis of auxiliary model based stochastic gradient parameter estimation for MIMO systems under weak conditions. Dynamics of Continuous Discrete and Impulsive Systems-Series A-Mathematical Analysis 13 Suppl (2006) 993-997 (Part 2)
16. Ding F., and Chen T. Performance analysis of multi-innovation gradient type identification methods. Automatica 43 1 (2007) 1-14
17. Ding F., Chen T., and Iwai Z. Adaptive digital control of Hammerstein nonlinear systems with limited output sampling. SIAM Journal on Control and Optimization 45 6 (2007) 2257-2276
18. Ding F., Shi Y., and Chen T. Auxiliary model based least-squares identification methods for Hammerstein output-error systems. Systems & Control Letters 5 56 (2007) 373-380
19. Mukaidani H., Xu H., and Mizukami K. New iterative algorithm for algebraic Riccati equation related to H infinity control problem of singularly perturbed systems. IEEE Transactions on Automatic Control 46 10 (2001) 1659-1666
20. Chu K.E. The solution of the matrix equations AXB - CXD = E and (YA - DZ, YC - BZ) = (E, F). Linear Algebra and Its Applications 93 (1987) 93-105
21. Xu G., Wei M., and Zheng D. On solutions of matrix equation AXB + CYD = F. Linear Algebra and Applications 279 1-3 (1998) 93-109
22. Golub G.H., Nash S., and Van Loan C.F. A Hessenberg-Schur method for the matrix problem AX + XB = C. IEEE Transactions on Automatic Control 24 6 (1979) 909-913