Gradient-based iterative algorithm for a class of the coupled matrix equations related to control systems

IET Control Theory and Applications

Volumn 8, Issue 15, 2014, Pages 1588-1595

  Ding, Feng ^a   Zhang, Huamin ^a  

^a JIANGNAN UNIVERSITY   (China)

Author keywords

[No Author keywords available]

Indexed keywords

ITERATIVE METHODS;

COUPLED MATRIX EQUATIONS; GRADIENT BASED; GRADIENT BASED ITERATIVE ALGORITHMS; GRADIENT SEARCH; ITERATIVE MATRICES; OBJECTIVE FUNCTIONS; OPTIMAL CONVERGENCE; SPECTRAL RADII;

MATRIX ALGEBRA;

EID: 84907330358     PISSN: 17518644     EISSN: 17518652     Source Type: Journal    
DOI: 10.1049/iet-cta.2013.1044     Document Type: Article

References (43)

1. Wu, A.G., Fu, Y.M., Duan, G.R.: 'On solutions of matrix equations V-AVF=BW and V-AV ¯F=BW', Math. Comput. Modell, 2008, 47, (11-12), pp. 1181-1197
2. Wu, A.G., Wang, H.Q., Duan, G.R.: 'On matrix equations X-AXF=C and X-AXF=C', J. Comput. Appl. Math., 2009, 230, (2), pp. 690-698
3. Wu, A.G., Duan, G.R.: 'Solution to the generalised Sylvester matrix equation AV + BW = AVF', IET Control Theory Appl., 2007, 1, (1), pp. 402-408
4. Dehghan, M., Hajarian M.: 'Efficient iterative method for solving the second-order Sylvester matrix equation EVF-AVF-CV=BW, IET Control Theory Appl., 2009, 3, (10), pp. 1401-1408
5. Li, Z.Y., Zhou, B., Wang, Y., Duan, G.R.: 'Numerical solution to linear matrix equation by finite steps iteration', IET Control Theory Appl., 2010, 4, (7), pp. 1245-1253
6. Liu, J.Z., Huang, Z.H., Zhu, L., Huang, Z.J.: 'Theorems on Schur complement of block diagonally dominant matrices and their application in reducing the order for the solution of large scale linear systems', Linear Algebra Appl., 2011, 435, (12), pp. 3085-3100
7. Wu, A.G., Feng, G., Duan, G.R., Liu, W.Q.: 'Iterative solutions to the Kalman-Yakubovich-conjugate matrix equation', Appl. Math. Comput, 2011, 217, (9), pp. 4427-4438
8. Liu, J.Z., Zhang, J., Liu, Y.: 'New solution bounds for the continuous algebraic Riccati equation', J. Franklin Inst. Eng. Appl. Math., 2011, 348, (8), pp. 2128-2141
9. Li, J.F., Hu, X.Y., Lei, Z.: 'New symmetry preserving method for optimal correction of damping and stiffness matrices using measured modes', J. Comput. Appl. Math., 2010, 234, (5), pp. 1572-1585
10. Ding, F., Chen, T.: 'Gradient based iterative algorithms for solving a class of matrix equations', IEEE Trans. Autom. Control, 2005, 50, (8), pp. 1216-1221
11. Ding, F., Chen, T.: 'On iterative solutions of general coupled matrix equations', SIAM J. Control Optim., 2006, 44, (6), pp. 2269-2284
12. Ding, F.: 'Coupled-least-squares identification for multivariable systems', IET Control Theory Appl., 2013, 7, (1), pp. 68-79
13. Ding, F, Liu, X.M., Chen, H.B., Yao, G.Y.: 'Hierarchical gradient based and hierarchical least squares based iterative parameter identification for CARARMA systems', Signal Process., 2014, 97, pp. 31-39
14. Ding, F, Deng, K.P., Liu, X.M.: 'Decomposition based Newton iterative identification method for a Hammerstein nonlinear FIR system with ARMA noise', Circuits Syst. Signal Process., 2014. doi: 10.1007/s00034-014-9772-y
15. Shi, Y., Yu, B.: 'Output feedback stabilization of networked control systems with random delays modeled by Markov chains', IEEE Trans. Autom. Control, 2009, 54, (7), pp. 1668-1674
16. Shi, Y., Yu, B.: 'Robust mixed H-2/H-infinity control of networked control systems with random time delays in both forward and backward communication links', Automatica, 2011, 47, (4), pp. 754-760
17. Li, H., Shi, Y.: 'Robust H-infinity filtering for nonlinear stochastic systems with uncertainties and random delays modeled by Markov chains', Automatica, 2012, 48, (1), pp. 159-166
18. Ding, F.: 'State filtering and parameter identification for state space systems with scarce measurements', Signal Process., 2014, 104, pp. 369-380
19. Ding, F.: 'Hierarchical parameter estimation algorithms for multi-variable systems using measurement information', Inf. Sci, 2014. http://dx.doi.org/10.1016/j.ins.2014.02.103
20. Liu, Y.J., Ding, F., Shi, Y.: 'An efficient hierarchical identification method for general dual-rate sampled-data systems', Automatica, 2014, 50, (3), 962-973
21. Ding, F.: 'Combined state and least squares parameter estimation algorithms for dynamic systems', Appl. Math. Modell., 2014, 38, (1), pp. 403-412
22. Ding, F., Liu, X.G., Chu.J.: 'Gradient-based and least-squares-based iterative algorithms for Hammerstein systems using the hierarchical identification principle', IET Control Theory Appl, 2013, 7, (2), pp. 176-184.
23. 1A = I', Appl. Math. Comput, 2013, 219, (14), pp. 7377-7391
24. Zhou, B., Duan, G.R.: 'An explicit solution to the matrix equation AX -XF = BY', Linear Algebra Appl., 2005, 402, pp. 345-366
25. 2', Appl. Math. Comput., 2011, 218, (7), pp. 3166-3175
26. Witula R., Roman, S., Slota, D., Kampik, M.: 'Some properties of the full matrices', Appl. Math. Comput., 2012, 219, (3), pp. 1222-1231
27. Ding, F., Chen, T.: 'Iterative least squares solutions of coupled Sylvester matrix equations', Syst. Control Lett., 2005, 54, (2), pp. 95-107
28. Ding, F., Liu, X.P., Ding, J.: 'Iterative solutions of the generalized Sylvester matrix equations by using the hierarchical identification principle', Appl. Math. Comput., 2008, 197, (1), pp. 41-50
29. Xie, L., Ding, J., Ding, F.: 'Gradient based iterative solutions for general linear matrix equations', Comput. Math. Appl., 2009, 58, (7), pp. 1441-1448
30. T D=F', Appl. Math. Comput., 2010, 217, (5), pp. 2191-2199
31. i', Comput. Math. Appl., 2010, 59, (11), pp. 3500-3507
32. Zhang, H.M., Ding, F.: 'A property of the eigenvalues of the symmetric positive definite matrix and the iterative algorithm for coupled Sylvester matrix equations', J. Franklin Institute-Eng. Appl. Math., 2014, 351, (1), pp. 340-357
33. Dehghan, M., Hajarian, M.: 'An iterative method for solving the generalized coupled Sylvester matrix equations over generalized bisym-metric matrices', Appl. Math. Modell., 2010, 34, (3), pp. 639-654
34. Dehghan, M., Hajarian, M.: 'Analysis of an iterative algorithm to solve the generalized coupled Sylvester matrix equations', Appl. Math. Modell., 2011, 35, (7), pp. 3285-3300
35. Wu, A.G., Lv, L.L., Hou, M.Z.: 'Finite iterative algorithms for extended Sylvester-conjugate matrix equations', Math. Comput. Modell., 2011, 54, (9-10), pp. 2363-2384
36. Wu, A.G., Zeng, X.L., Duan, G.R., Wu, W.J.: 'Iterative solutions to the extended Sylvester-conjugate matrix equatinos', Appl. Math. Comput., 2010, 217, (1), pp. 130-142
37. Wu, A.G., Feng, G., Duan, G.R., Wu, W.J.: 'Iterative solutions to coupled Sylvester-conjugate matrix equations', Comput. Math. Appl., 2010, 60, (1), pp. 54-66
38. Zhou, B., Li, Z.Y., Duan, G.R., Wang, Y.: 'Weighted least squares solutions to general coupled Sylvester matrix equations', J. Comput. Appl. Math., 2009, 224, (2), pp. 759-776
39. Li, Z.Y., Wang, Y., Zhou, B., Duan, G.R.: 'Least squares solution with the minimum-norm to general matrix equations via iteration', Appl. Math. Comput., 2010, 215, (10), pp. 3547-3562
40. 2 and a matrix programming problem', Linear Algebra Appl., 1990, 131, pp. 107-123
41. 2 with applications', Comput. Math. Appl., 2011, 41, (7-8), pp. 929-935
42. Liao, A.P., Lei, Y.: 'Least-squares solution with the minimum-norm for the matrix equation (AXB,GXH) = (C, D)', Comput. Math. Appl., 2005, 50, (3-4), pp. 539-549
43. Yuan, S.F., Liao, A.P., Lei, Y.: 'Least squares Hermitian solution of the matrix equation (AXB,CXD) = (E,F) with the least norm over the skew field of quaternion', Math. Comput. Modell., 2008, 48, (1-2), pp. 91-100