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Weak regularizability and pole assignment for non-square linear systems
Kybernetika, Tome 48 (2012) no. 6, pp. 1065-1088 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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.
Classification : 93B52, 93B55, 93C05
Keywords: linear systems; linear state feedback; pole assignment 
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Korotka, Tetiana; Loiseau, Jean Jacques; Zagalak, Petr. Weak regularizability and pole assignment for non-square linear systems. Kybernetika, Tome 48 (2012) no. 6, pp. 1065-1088. http://geodesic.mathdoc.fr/item/KYB_2012_48_6_a0/

[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 | MR | Zbl

[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 | Zbl

[4] Kailath, T.: Linear systems. Englewood Cliffs, Prentice Hall, NJ 1980. | MR | Zbl

[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 | MR | Zbl

[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

[9] Loiseau, J. J., Özçaldiran, K., Malabre, M., Karcanias, N.: Feedback canonical forms of singular systems. Kybernetika 27 (1991), 4, 289-305. | MR | Zbl

[10] Loiseau, J. J., Zagalak, P.: On pole structure assignment in linear systems. Internat. J. Control 82 (2009), 7, 1179-1192. | DOI | MR | Zbl

[11] Özçaldiran, K., Lewis, F. L.: On the regularizability of singular systems. IEEE Trans. Automat. Control 35 (1990), 10, 1156-1160. | DOI | MR | Zbl

[12] Rosenbrock, R. R.: State-space and Multivariable Theory. Nelson, London 1970. | Zbl

[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 | MR

[14] Zaballa, I.: Interlacing inequalities and control theory. Lin. Algebra Appl. 101 (1988), 9-31. | DOI | MR | Zbl