Equivalent Condition for Poles Assignability via Decentralized Static Output Feedback

Article Preview

Abstract:

This paper deals with difficulty of decentralization and presents an equivalent condition for poles assignability via decentralized static output feedback based on Kronecker product and vectorization. This condition is an equation regarding a nonsingular matrix variable and doesn't concern feedback gains. Consequently, an explanation is given for decentralized assignability, and results of centralized case are also obtained as corollaries of the proposed condition.

You might also be interested in these eBooks

Info:

Periodical:

Advanced Materials Research (Volumes 546-547)

Pages:

910-915

Citation:

Online since:

July 2012

Authors:

Export:

Price:

Permissions CCC:

Permissions PLS:

Сopyright:

© 2012 Trans Tech Publications Ltd. All Rights Reserved

Share:

Citation:

[1] Kaiyang Yang and Robert Orsi, Generalized pole placement via static output feedback: A methodology based on projections, Automatica, Vol. 42, December 2006, pp.2143-2150.

DOI: 10.1016/j.automatica.2006.06.021

Google Scholar

[2] Guangying Zhang and Alexander Lanzon, Relationship between poles and zeros of input-output and chain-scattering systems Systems & Control Letters, Vol. 55, April 2006, pp.314-320.

DOI: 10.1016/j.sysconle.2005.08.007

Google Scholar

[3] Runyi Yu and Dianhui Wang, Structural properties and poles assignability of LTI singular systems under output feedback, Automatica, Vol. 39, April 2003, pp.685-692.

DOI: 10.1016/s0005-1098(02)00283-2

Google Scholar

[4] Sanqing Hu and Jun Wang, A gradient flow approach to on-line robust pole assignment for synthesizing output feedback control systems, Automatica, Vol. 38, November 2002, p.1959-(1968).

DOI: 10.1016/s0005-1098(02)00144-9

Google Scholar

[5] A. Eremenko and A. Gabrielov, Counterexamples to pole placement by static output feedback, Linear Algebra and its Applications, Vol. 15, August 2002, pp.211-218.

DOI: 10.1016/s0024-3795(01)00443-8

Google Scholar

[6] K. H. Kiritsis, A necessary condition for pole assignment by constant output feedback, Systems & Control Letters, Vol. 45, April 2002, pp.317-320.

DOI: 10.1016/s0167-6911(01)00192-x

Google Scholar

[7] Danchi Jiang and Jun Wang, Augmented gradient flows for on-line robust pole assignment via state and output feedback, Automatica, Vol. 38, February 2002, pp.279-286.

DOI: 10.1016/s0005-1098(01)00200-x

Google Scholar

[8] Chia-chi Tsui, A new dynamic output feedback compensator design for pole assignment, Journal of the Franklin Institute, Vol. 336, May 1999, pp.665-674.

DOI: 10.1016/s0016-0032(98)00008-8

Google Scholar

[9] Dan-chi Jiang and J. B. Moore, Least squares pole assignment by memoryless output feedback , Systems & Control Letters, Vol. 29, September 1996, pp.31-42.

DOI: 10.1016/0167-6911(96)00044-8

Google Scholar

[10] John Leventides and Nicos Karcanias, Global asymptotic linearisation of the pole placement map: a closed-form solution for the constant output feedback problem, Automatica, Vol. 31, September 1995, pp.1303-1309.

DOI: 10.1016/0005-1098(95)00047-z

Google Scholar

[11] John Leventides and Nicos Karcanias, A new sufficient condition for arbitrary pole placement by real constant output feedback, Systems & Control Letters, Vol. 18, March 1992, pp.191-199.

DOI: 10.1016/0167-6911(92)90005-d

Google Scholar

[12] Leventides, J.; Karcanias, N. Sufficient conditions for pole assignment under decentralised output feedback, Proceedings of IEEE Conference on Decision and Control, Dec. 1993, p.3756 – 3761.

DOI: 10.1109/cdc.1993.325920

Google Scholar

[13] Djaferis, T.; Narayana, A. A new sufficient condition for generic pole assignment by output feedback;, IEEE Transactions on Automatic Control, Vol. 30, Mar 1985, p.280 – 283.

DOI: 10.1109/tac.1985.1103928

Google Scholar

[14] V. L. Syrmos, C. T. Abdallah, and K. Grigoriadis, Static output feedback-a survey, Automatica, vol. 33, 1997, pp.125-137.

DOI: 10.1016/s0005-1098(96)00141-0

Google Scholar

[15] A. Trofino-Neto and V. Kucera, Stabilization via static output feedback, IEEE Trans. Autom. Control, vol. 38, 1993, pp.764-765.

DOI: 10.1109/9.277243

Google Scholar

[16] V. Kucera and C. de Souza, A necessary and sufficient condition for output feedback stabilizability, Automatica, vol. 10, 1995, pp.1357-1359.

DOI: 10.1016/0005-1098(95)00048-2

Google Scholar

[17] G. Garcia, B. Pradin, and F. Zeng, Stabilization of discrete time linear systems by static output feedback, IEEE Trans. Autom. Control, vol. 46, 2001, p.1954-(1958).

DOI: 10.1109/9.975499

Google Scholar

[18] J. C. Geromel, C. C. deSouza, and R. E. Skelton, Static output feedback controllers: Stability and convexity, IEEE Trans. Autom. Control, vol. 43, 1998, pp.120-125.

DOI: 10.1109/9.654912

Google Scholar

[19] D. Henrion and J. B. Lasserre, Convergent relaxations of polynomial matrix inequalities and static output feedback, IEEE Trans. Autom. Control, vol. 51, 2006, pp.192-202.

DOI: 10.1109/tac.2005.863494

Google Scholar

[20] J. C. Geromel, P. L. D. Peres, and S. R. Souza, Convex analysis of output feedback control problems: Robust stability and performance, IEEE Trans. Autom. Control, vol. 41, 1996, pp.997-1003.

DOI: 10.1109/9.508904

Google Scholar

[21] L. E. Ghaoui, F. Oustry, and M. Ait Rami, A cone complementarity linearization algorithm for static output-feedback and related problems, IEEE Trans. Autom. Control, vol. 42, 1997, pp.1171-1175.

DOI: 10.1109/9.618250

Google Scholar

[22] Y. -Y. Cao, J. Lam, and Y. X. Sun, Static output feedback stabilization: An ILMI approach, Automatica, vol. 34, 1998, pp.1641-1645.

DOI: 10.1016/s0005-1098(98)80021-6

Google Scholar

[23] F. Leibfritz, An LMI-based algorithm for designing suboptimal static output feedback controllers, SIAM. J. Control Optim., vol. 39, 2001, pp.1711-1735.

DOI: 10.1137/s0363012999349553

Google Scholar

[24] A. Graham, Kronecker Products and Matrix Calculus with Applications, Chichester, West Sussex. England: Ellis Honvood. (1981).

Google Scholar

[25] Fletcher LR, Some necessary and sufficient condition for eigenstructure assignment, International Journal of Control, Vol. 42, 1985, pp.1457-1468.

DOI: 10.1080/00207178508933437

Google Scholar