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Partial eigenvalue assignment with time delay robustness
1. | Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China, China |
References:
[1] |
M. Arnold and B. N. Datta, Single-input eigenvalue assignment algorithms: A close look, SIAM J. Matrix Anal. Appl., 19 (1998), 444-467.
doi: 10.1137/S0895479895294885. |
[2] |
R. Byers and S. G. Nash, Approaches to robust pole assignment, International Journal of Control, 49 (1989), 97-117. |
[3] |
D. Calvetti, B. Lewis and L. Reichel, On the solution of the single input pole placement problem, Mathematical Theory of Networks and Systems (MTNS 98)(Eds: A. Beghi, L. Finesso and G. Picci), Il Poliografo, Padova, (1998), 585-588. |
[4] |
D. Calvetti, B. Lewis and L. Reichel, On the selection of poles in the single input pole placement problem, Linear Algebra Appl., 302/303 (1999), 331-345.
doi: 10.1016/S0024-3795(99)00123-8. |
[5] |
D. Calvetti, B. Lewis and L. Reichel, Partial eigenvalue assignment for large linear control systems, Contemporary Mathematics, American Mathematical Society, Providence, RI, 28 (2001), 241-254. |
[6] |
B. N. Datta, "Numerical Methods for Linear Control Systems Design and Analysis," Elsevier Academic Press, New York, 2003. |
[7] |
B. N. Datta, An algorithm to assign eigenvalues in a Hessenberg matrix, IEEE Transactions on Automatic Control, AC-32 (1987), 414-417.
doi: 10.1109/TAC.1987.1104622. |
[8] |
B. N. Datta and Y. Saad, Arnoldi methods for large Sylvester-like observer matrix equations and an associated algorithm for partial spectrum assignment, Linear Algebra Appl., 154/156 (1991), 225-244. |
[9] |
B. N. Datta and D. R. Sarkissian, Partial eigenvalue assignment in linear systems: existence, uniqueness and numerical solution, Proceedings of the Mathematical Theory of Networks and Systems (MTNS), Notre Dame, August 2002. |
[10] |
T. Hu and J. Lam, On optimizing performance indices with pole assignment constraints, Journal of System Control Engineering, 212 (1998), 327-337. |
[11] |
J. Kautsky, N. K. Nichols and P. Van Dooren, Robust pole assignment in linear state feedback, International Journal of Control, 41 (1985), 1129-1155.
doi: 10.1080/0020718508961188. |
[12] |
J. Lam and W. Yan, A gradient flow approach to robust pole-placement problem, International Journal of Robust Nonlinear Control, 5 (1995), 175-185.
doi: 10.1002/rnc.4590050303. |
[13] |
J. Lam and W. Yan, Pole assingnment with optimal spectral conditioning, Systems Control Letters, 29 (1997), 241-253.
doi: 10.1016/S0167-6911(97)90007-4. |
[14] |
J. Lam, W. Yan and T. Hu, Pole assignment with eigenvalue and stability robustness, International Journal of Control, 72 (1999), 1165-1174.
doi: 10.1080/002071799220326. |
[15] |
V. Mehrmann and H. Xu, An analysis of the pole placement problem I. The single-input case, Electron. Trans. Numer. Anal., 4 (1996), 89-105. |
[16] |
V. Mehrmann and H. Xu, An analysis of the pole placement problem II. The multi-input case, Electron. Trans. Numer. Anal., 5 (1997), 77-97. |
[17] |
V. Mehrmann and H. Xu, Choosing poles so that the single-input pole placement is well conditioned, SIAM J. Matrix Anal. Appl., 19 (1998), 664-681.
doi: 10.1137/S0895479896302382. |
[18] |
G. Miminis and C. C. Paige, An algorithm for pole assignment of time invariant linear systems, International Journal of Control, 35 (1982), 341-354.
doi: 10.1080/00207178208922623. |
[19] |
G. Miminis and H. Roth, Algorithm 747: A Fortran subroutine to solve the eigenvalue assignment problem for multiinput systems using state feedback, ACM Trans. Math. Software, 21 (1995), 299-326.
doi: 10.1145/210089.210094. |
[20] |
N. K. Nichols, Robustness in partial pole placement, IEEE Transactions on automatic control, AC-32 (1987), 728-732.
doi: 10.1109/TAC.1987.1104703. |
[21] |
T. J. Owens and J. O'Reilly, Parametric state-feedback control for arbitrary eigenvalue assignment with minimum sensitivity, IEE Proceedings D, 136 (1989), 307-313. |
[22] |
B. Porter and R. Crossley, "Model Control: Theory and Applications," Barnes Noble, New York, 1972. |
[23] |
Y. M. Ram, A. Singh and J. E. Mottershead, State feedback control with time delay, Mechanical Systems and Signal Processing, 23 (2009), 1940-1945.
doi: 10.1016/j.ymssp.2008.04.012. |
[24] |
Y. Saad, Projection and deflation methods for partial pole assignment in linear state feedback, IEEE Transactions on Automatic Control, 33 (1988), 290-297.
doi: 10.1109/9.406. |
[25] |
D. R. Sarkissian, "Theory and Computations of Partial Eigenvalue and Eigenstructure Assignment Problems in Matrix Second-order and Distributed-parameter Systems", Ph.D thesis, Northerm Illinnois University, 2001. |
[26] |
X. Shi and Y. Wei, A sharp version of Bauer-Fike's theorem, J. Comput. Appl. Math., 236 (2012), 3218-3227.
doi: 10.1016/j.cam.2012.02.021. |
[27] |
E. De Souza and S. P. Bhattacharyya, Controllability, observability and the solution of AX-XB=C , Linear Algebra Appl., 39 (1981), 167-188.
doi: 10.1016/0024-3795(81)90301-3. |
[28] |
J. G. Sun, On numerical methods for robust pole assignment in control system design, J. Comput. Math., 5 (1987), 119-134. |
[29] |
J. G. Sun, On numerical methods for robust pole assignment in control system design II, J. Comput. Math., 5 (1987), 352-363. |
[30] |
J. G. Sun, On measures of robustness of a control system, Math. Numer. Sinica(In Chinese), 9 (1987), 319-326. |
[31] |
A. Varga, A Schur method for pole assignment, IEEE Transactions on Automatic Control, AC-26b (1981), 517-519.
doi: 10.1109/TAC.1981.1102605. |
[32] |
A. Varga, Robust pole assignment via Sylvester equation based state feedback parameterization, Proceedings of the 2000 IEEE International Symposium on Computer-Aided Control System Design, Anchorage, Alaska, USA, 2000. |
show all references
References:
[1] |
M. Arnold and B. N. Datta, Single-input eigenvalue assignment algorithms: A close look, SIAM J. Matrix Anal. Appl., 19 (1998), 444-467.
doi: 10.1137/S0895479895294885. |
[2] |
R. Byers and S. G. Nash, Approaches to robust pole assignment, International Journal of Control, 49 (1989), 97-117. |
[3] |
D. Calvetti, B. Lewis and L. Reichel, On the solution of the single input pole placement problem, Mathematical Theory of Networks and Systems (MTNS 98)(Eds: A. Beghi, L. Finesso and G. Picci), Il Poliografo, Padova, (1998), 585-588. |
[4] |
D. Calvetti, B. Lewis and L. Reichel, On the selection of poles in the single input pole placement problem, Linear Algebra Appl., 302/303 (1999), 331-345.
doi: 10.1016/S0024-3795(99)00123-8. |
[5] |
D. Calvetti, B. Lewis and L. Reichel, Partial eigenvalue assignment for large linear control systems, Contemporary Mathematics, American Mathematical Society, Providence, RI, 28 (2001), 241-254. |
[6] |
B. N. Datta, "Numerical Methods for Linear Control Systems Design and Analysis," Elsevier Academic Press, New York, 2003. |
[7] |
B. N. Datta, An algorithm to assign eigenvalues in a Hessenberg matrix, IEEE Transactions on Automatic Control, AC-32 (1987), 414-417.
doi: 10.1109/TAC.1987.1104622. |
[8] |
B. N. Datta and Y. Saad, Arnoldi methods for large Sylvester-like observer matrix equations and an associated algorithm for partial spectrum assignment, Linear Algebra Appl., 154/156 (1991), 225-244. |
[9] |
B. N. Datta and D. R. Sarkissian, Partial eigenvalue assignment in linear systems: existence, uniqueness and numerical solution, Proceedings of the Mathematical Theory of Networks and Systems (MTNS), Notre Dame, August 2002. |
[10] |
T. Hu and J. Lam, On optimizing performance indices with pole assignment constraints, Journal of System Control Engineering, 212 (1998), 327-337. |
[11] |
J. Kautsky, N. K. Nichols and P. Van Dooren, Robust pole assignment in linear state feedback, International Journal of Control, 41 (1985), 1129-1155.
doi: 10.1080/0020718508961188. |
[12] |
J. Lam and W. Yan, A gradient flow approach to robust pole-placement problem, International Journal of Robust Nonlinear Control, 5 (1995), 175-185.
doi: 10.1002/rnc.4590050303. |
[13] |
J. Lam and W. Yan, Pole assingnment with optimal spectral conditioning, Systems Control Letters, 29 (1997), 241-253.
doi: 10.1016/S0167-6911(97)90007-4. |
[14] |
J. Lam, W. Yan and T. Hu, Pole assignment with eigenvalue and stability robustness, International Journal of Control, 72 (1999), 1165-1174.
doi: 10.1080/002071799220326. |
[15] |
V. Mehrmann and H. Xu, An analysis of the pole placement problem I. The single-input case, Electron. Trans. Numer. Anal., 4 (1996), 89-105. |
[16] |
V. Mehrmann and H. Xu, An analysis of the pole placement problem II. The multi-input case, Electron. Trans. Numer. Anal., 5 (1997), 77-97. |
[17] |
V. Mehrmann and H. Xu, Choosing poles so that the single-input pole placement is well conditioned, SIAM J. Matrix Anal. Appl., 19 (1998), 664-681.
doi: 10.1137/S0895479896302382. |
[18] |
G. Miminis and C. C. Paige, An algorithm for pole assignment of time invariant linear systems, International Journal of Control, 35 (1982), 341-354.
doi: 10.1080/00207178208922623. |
[19] |
G. Miminis and H. Roth, Algorithm 747: A Fortran subroutine to solve the eigenvalue assignment problem for multiinput systems using state feedback, ACM Trans. Math. Software, 21 (1995), 299-326.
doi: 10.1145/210089.210094. |
[20] |
N. K. Nichols, Robustness in partial pole placement, IEEE Transactions on automatic control, AC-32 (1987), 728-732.
doi: 10.1109/TAC.1987.1104703. |
[21] |
T. J. Owens and J. O'Reilly, Parametric state-feedback control for arbitrary eigenvalue assignment with minimum sensitivity, IEE Proceedings D, 136 (1989), 307-313. |
[22] |
B. Porter and R. Crossley, "Model Control: Theory and Applications," Barnes Noble, New York, 1972. |
[23] |
Y. M. Ram, A. Singh and J. E. Mottershead, State feedback control with time delay, Mechanical Systems and Signal Processing, 23 (2009), 1940-1945.
doi: 10.1016/j.ymssp.2008.04.012. |
[24] |
Y. Saad, Projection and deflation methods for partial pole assignment in linear state feedback, IEEE Transactions on Automatic Control, 33 (1988), 290-297.
doi: 10.1109/9.406. |
[25] |
D. R. Sarkissian, "Theory and Computations of Partial Eigenvalue and Eigenstructure Assignment Problems in Matrix Second-order and Distributed-parameter Systems", Ph.D thesis, Northerm Illinnois University, 2001. |
[26] |
X. Shi and Y. Wei, A sharp version of Bauer-Fike's theorem, J. Comput. Appl. Math., 236 (2012), 3218-3227.
doi: 10.1016/j.cam.2012.02.021. |
[27] |
E. De Souza and S. P. Bhattacharyya, Controllability, observability and the solution of AX-XB=C , Linear Algebra Appl., 39 (1981), 167-188.
doi: 10.1016/0024-3795(81)90301-3. |
[28] |
J. G. Sun, On numerical methods for robust pole assignment in control system design, J. Comput. Math., 5 (1987), 119-134. |
[29] |
J. G. Sun, On numerical methods for robust pole assignment in control system design II, J. Comput. Math., 5 (1987), 352-363. |
[30] |
J. G. Sun, On measures of robustness of a control system, Math. Numer. Sinica(In Chinese), 9 (1987), 319-326. |
[31] |
A. Varga, A Schur method for pole assignment, IEEE Transactions on Automatic Control, AC-26b (1981), 517-519.
doi: 10.1109/TAC.1981.1102605. |
[32] |
A. Varga, Robust pole assignment via Sylvester equation based state feedback parameterization, Proceedings of the 2000 IEEE International Symposium on Computer-Aided Control System Design, Anchorage, Alaska, USA, 2000. |
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