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Pole placement and related problems. (English) Zbl 0762.93037
Summary: We survey recent work in pole placement and related problems which are notably matrix completion, placement of the zeroes of a triple and feedback simulation. For each of these points we examine the existing and open field, and we point out the connection with pole placement by the use of matrix pencil formulation.

MSC:
93B55 Pole and zero placement problems
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References:
[1] J. Descusse J.F. Lafay, M. Malabre: Solution to Morgan’s problem. IEEE Trans. Automat. Control AC-33 (1988), 8, 732 - 739. · Zbl 0656.93018 · doi:10.1109/9.1289
[2] G. Gantmacher: Theorie des Matrices. Dunod, Paris 1966. · Zbl 0136.00410
[3] M. Heymann: Controllability indices and feedback simulation. SIAM J. Control Optim. 14 (1976), 4, 769 - 789. · Zbl 0354.93026 · doi:10.1137/0314050
[4] V. Kučera: Assigning the invariant factors by feedback. Kybernetika 17 (1981), 2, 118 - 127. · Zbl 0478.93014
[5] V. Kučera, P. Zagalak: Fundamental of state feedback for singular systems. Automatica 24 (1988), 5, 653 - 658. · Zbl 0661.93033
[6] V. Kučera: Invariant factors and feedback control. Proc. IEEE Internat. Symposium on Circuits and Systems, Roma, May 10 - 12, 1982.
[7] J.J. Loiseau: Some geometric considerations about the Kronecker normal form. Internat. J. Control 42 (1985), 6, 1411 - 1431. · Zbl 0609.93014 · doi:10.1080/00207178508933434
[8] J.J. Loiseau: Structural necessary conditions for model following problem. Proceedings of the 1st European Control Conf., Grenoble, 1991. Hermes, Paris, 1991, pp. 703 - 708.
[9] J.J. Loiseau: Sur la modification de la structure a l’infini par un retour d’état statique. SIAM J. Control Optim. 26 (1988), 2, 251 - 273. · Zbl 0643.93016 · doi:10.1137/0326015
[10] J.J. Loiseau K. Ozcaldiran M. Malabre, N. Karcanias: Feedback canonical forms of singular systems. Kybernetika 27 (1991), 4, 289 - 305. · Zbl 0767.93007
[11] H.H. Rosenbrock: State Space and Multivariate Theory. Wiley, New York 1970. · Zbl 0246.93010
[12] A.S. Morse: Structural invariants of linear multivariable systems. SIAM J. Control Optim. 11 (1973), 3, 446 - 465. · Zbl 0259.93011 · doi:10.1137/0311037
[13] M. Schieguer: A generalization of Rosenbrock’s theorem. IEEE Trans. Automat. Control AC-32 (1987), 2, 155.
[14] I. Zaballa: Matrices with prescribed rows and invariant factors. Linear Algebra Appl. 87 (1987), 113- 146. · Zbl 0632.15003 · doi:10.1016/0024-3795(87)90162-5
[15] I. Zaballa: Interlacing inequalities and control theory. Linear Algebra Appl. 101 (1988), 9 - 31. · Zbl 0673.93025 · doi:10.1016/0024-3795(88)90140-1
[16] P. Zagalak, V. Kučera: Fundamental theorem of proportional state feedback for descriptor systems. Kybernetika 28 (1992), 1, 81 - 89. · Zbl 0762.93049 · www.kybernetika.cz · eudml:28932
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