Explicit general solution to the matrix equation AV+BW=EVF+R

IET Control Theory and Applications

Volumn 2, Issue 1, 2008, Pages 56-60

  Wu, A G ^a,b   Duan, G R ^a  

^a HARBIN INSTITUTE OF TECHNOLOGY   (China)

^b Shenzhen University Town   (China)

Author keywords

[No Author keywords available]

Indexed keywords

CONVERGENCE OF NUMERICAL METHODS; EIGENVALUES AND EIGENFUNCTIONS; MATHEMATICAL TRANSFORMATIONS; POLYNOMIALS; SINGULAR VALUE DECOMPOSITION;

ELEMENTARY TRANSFORMATIONS; JORDAN MATRIX; MATRIX EQUATION;

CONTROL SYSTEMS;

EID: 38649114664     PISSN: 17518644     EISSN: 17518652     Source Type: Journal    
DOI: 10.1049/iet-cta:20070083     Document Type: Article

References (20)

1. Liu, G.P., and Patton, R.J.: ' Robust eigenstructure assignment for descriptor systems ', Int. J. Syst. Sci., 1998, 29, (1), p. 75-84 10.1080/00207729808929498 0020-7721
2. Duan, G.R.: ' Solution to matrix equation AV+BW=EVF and eigenstructure assignment for descriptor systems ', Automatica, 1992, 28, (3), p. 639-643 10.1016/0005-1098(92)90191-H 0005-1098
3. Wu, A.G., and Duan, G.R.: ' Design of PD observers in descriptor linear systems ', Int. J. Control, Autom., Syst., 2007, 5, (1), p. 93-98 1598-6446
4. Bhattacharyya, S.P., and De Souza, E.: ' Pole assignment via Sylvester equation ', Syst. Control Lett., 1982, 17, p. 261-263 0167-6911
5. Keel, L.H., Flemingn, J.A., and Bhattacharyys, S.P.: ' Minimum norm pole assignment via Sylvester's equation ', Linear Algebr Role Syst. Theory, 1985, 47, p. 265-272
6. Duan, G.R.: ' Solution of the equation AV+BW=VF and their application to eigenstructure assignment in linear systems ', IEEE Trans. Autom. Control, 1993, 38, (2), p. 276-280 10.1109/9.250470 0018-9286
7. Duan, G.R., Liu, G.P., and Thompson, S.: ' Eigenstructure assignment design for proportional-integral observers: continuous-time cas ', IEE Proc. Control Theory Appl., 2001, 148, (3), p. 263-267 10.1049/ip-cta:20010428 1350-2379
8. Van Dooren, P.: ' Reduced order observers: a new algorithm and proof ', Syst. Control Lett., 1984, 19, (4), p. 243-251 0167-6911
9. Datta, B., and Sarkissian, D.: ' Block algorithm for state estimation and functional observers ', Proc. IEEE Int. Symp. on Computer-Aided Control Systems Design, Ancorage, 2000, p. 19-23
10. Carvalho, J., Datta, K., and Hong, Y.: ' A new algorithm for full-rank solution of the Sylvester-observer equation ', IEEE Trans. Autom. Control, 2003, 48, (12), p. 2223-2228 10.1109/TAC.2003.820150 0018-9286
11. Datta, B., and Saad, Y.: ' Arnoldi methods for large Sylvester-like observer matrix equations, and associated algorithm for partial spectrum assignment ', Linear Algebr Appl., 1991, 154/156, p. 225-244 0024-3795
12. Calvetti, D., Lewis, B., and Reichel, L.: ' On the solution of Sylvester-observer equation ', Num. Linear Algebr Appl., 2001, 8, (6-7), p. 435-452
13. Bischof, C., Datta, B., and Purkayastha, A.: ' A parallel algorithm for the Sylvester observer equation ', SIAM J. Sci. Comp., 1996, 17, p. 686-698 10.1137/S1064827591223276
14. Kautsky, J., Nichols, N.K., and Van Dooren, P.: ' Robust pole assignment in linear state feedback ', Int. J. Contrib., 1985, 41, (5), p. 1129-1155
15. Zhou, B., and Duan, G.R.: ' An explicit solution to the matrix equation AX-XF=BY ', Linear Algebr Appl., 2005, 402, p. 345-366 0024-3795
16. Tsui, C.C.: ' A complete analytical solution to the equation TA-FT=LC and its applications ', IEEE Trans. Autom. Control, 1987, 32, p. 742-744 0018-9286
17. Duan, G.R.: ' On the solution to Sylvester matrix equation AV+BW=EVF ', IEEE Trans. Autom. Control, 1996, 41, (4), p. 612-614 10.1109/9.489286 0018-9286
18. Duan, G.R., and Liu, G.P.: ' Complete parametric approach for eigenstructure assignment in a class of second-order linear systems ', Automatica, 2002, 38, (4), p. 725-729 10.1016/S0005-1098(01)00251-5 0005-1098
19. Duan, G.R., and Thompson, S.: ' Complete parametric solution to the matrix equation AV+BW=EVJ+R ', Proc. 38th Conference on Decision and Control, Phoenix, Arizons, USA, December, 1999, p. 2742-2743
20. Duan, G.R.: ' The solution to the matrix equation AV+BW=EVJ+R ', Appl. Math. Lett., 2004, 17, (10), p. 1197-1202 0893-9659