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Keywords:
linear systems; linear state feedback; pole assignment
linear systems; linear state feedback; pole assignment
Summary:
The problem of pole assignment by state feedback in the class of non-square linear systems is considered in the paper. It is shown that the problem is solvable under the assumption of weak regularizability, a newly introduced concept that can be viewed as a generalization of the regularizability of square systems. Necessary conditions of solvability for the problem of pole assignment are established. It is also shown that sufficient conditions can be derived in some special cases. Some conclusions and prospects for further studies are drawn in the last section.
References:
[1] Bacos, R., Cury, J. E. R., Loiseau, J. J.: Control of a class of constrained implicit systems. In: Proc. IFAC Symposium on System Structure and Control, Ancona 2010.
[2] Ishihara, J. Y., Terra, M. H.: Impulse controllability and observability of rectangular descriptor systems. IEEE Trans. Automat. Control 46 (2001), 6, 991-994. DOI 10.1109/9.928613 | MR 1836508 | Zbl 1007.93006
[3] Kaczorek, T.: Infinite eigenvalue assignment by an output feedback for singular systems. Internat. J. Appl. Math. Comput. Sci. 14 (2004), 1, 19-23. MR 2043575 | Zbl 1171.93331
[4] Kailath, T.: Linear systems. Englewood Cliffs, Prentice Hall, NJ 1980. MR 0569473 | Zbl 0870.93013
[5] Korotka, T., Loiseau, J. J., Zagalak, P.: A note on pole assignment in linear singular systems. In: Proc. 11th International Ph.D. Workshop on Systems and Control, Veszprem 2010.
[6] Kučera, V., Zagalak, P.: Fundamental theorem of state feedback for singular systems. Automatica 24 (1988), 5, 653-658. DOI 10.1016/0005-1098(88)90112-4 | MR 0966689 | Zbl 0661.93033
[7] Libeau, L.: Sur l'utilisation des divoï des pour la commande des systèmes à événements discrets. Ph.D. Thesis, Ecole Centrale de Nantes 1996.
[8] Liu, G. P., Patton, R. J.: Eigenstructure Assignment for Control System Design. John Wiley and Sons, New York 1998. MR 1606139
[9] Loiseau, J. J., Özçaldiran, K., Malabre, M., Karcanias, N.: Feedback canonical forms of singular systems. Kybernetika 27 (1991), 4, 289-305. MR 1127906 | Zbl 0767.93007
[10] Loiseau, J. J., Zagalak, P.: On pole structure assignment in linear systems. Internat. J. Control 82 (2009), 7, 1179-1192. DOI 10.1080/00207170802400954 | MR 2532197 | Zbl 1168.93009
[11] Özçaldiran, K., Lewis, F. L.: On the regularizability of singular systems. IEEE Trans. Automat. Control 35 (1990), 10, 1156-1160. DOI 10.1109/9.58561 | MR 1073262 | Zbl 0724.93011
[12] Rosenbrock, R. R.: State-space and Multivariable Theory. Nelson, London 1970. Zbl 0246.93010
[13] Vardulakis, A. I. G., Limebeer, D. N. J., Karcanias, N.: Structure and Smith-McMillan form of a rational matrix at infinity. Internat. J. Control 35 (1982), 4, 701-725. DOI 10.1080/00207178208922649 | MR 0669973
[14] Zaballa, I.: Interlacing inequalities and control theory. Lin. Algebra Appl. 101 (1988), 9-31. DOI 10.1016/0024-3795(88)90140-1 | MR 0941293 | Zbl 0673.93025
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