Sommario
Viene presentato un algoritmo per la trasformazione della matrice dinamica di sistemi lineari a più variabili di ingresso-uscita da forma “companion” generalizzata in forma di Jordan.
Il procedimento è basato su una trasformazione preliminare in forma canonica “ a catene di massima lunghezza” (MLCGCF) e sulla conoscenza degli autovalori e della loro multeplicità.
Summary
An algorithm for the transformation of generalized Companion forms for multivariable linear systems to Jordan form is considered.
The procedure is based on a preliminary transformation to the corresponding maximum length chains canonical form (MLCGCF) and on knowledge of the eigenvalues and their multiplicity.
References
F. R. Gantmacher,The theory of matrices, Chelsea Publ. Co., New York, 1959.
P. R. Halmos,Finite-dimensional vector spaces, Van Nostrand Reinhold, 1958.
K. Ogata,State space analysis of control systems, Prentice-Hall, Englewood Cliffs, N. J., 1967.
W. M. Wonham andC. D. Johnson,A note on the transformation to canonical (phase-variable) form, IEEE Trans. on A. C., Vol. AC-9, pp. 312–313, July 1964.
C. F. Chen andH. Chu,A matrix for evaluating Schwarz's form, IEEE Trans. on A. C., Vol. AC-11, pp. 303–305, April 1966.
I. G. Sarma, M. A. Pai andR. Viswanathan,A note on the transformation from Schwarz to Jordan canonical form, IEEE Trans. on A. C., Vol. AC-13, pp. 310–311, June 1968.
I. G. Sarma, M. A. Pai andR. Viswanathan,On the transformation to Schwarz canonical form, IEEE Trans. on A.C., Vol. AC-13, pp. 311–312, June 1968.
A. Graham,A note on a transformation between two canonical forms in state-space in terms of the eigenvalues of the system matrix, IEEE Trans. on A. C., Vol. AC-13, p. 448, August 1968.
B. Ramaswami andK. Ramar,Transformation to the phasevariable canonical form, IEEE Trans. on A. C., Vol. AC-13, pp. 746–747, Dec. 1968.
H. M. Power,Canonical form for the matrices of linear discretetime systems, Proc. IEE, Vol. 116, no. 7, July 1969.
C. E. Langenhop,On the stabilization of linear systems, Proc. Am. Math. Soc., Vol. 15, pp. 735–742, 1964.
D. G. Luengerger,Canonical forms for linear multivariable systems, IEEE Trans. on A. C., Vol. AC-12, pp. 290–293, June 1967.
R. S. Bucy,Canonical forms for multivariable systems, IEEE Trans. on A. C., Vol. AC-13, pp. 567–569, Oct. 1968.
C. Bonivento andR. Guidorzi,Canonical forms and linear systems identification, Int. Rept. no. 7, Institute of Automatics, University of Bologna, Sept. 1970.
C. Bonivento andR. Guidorzi,Canonical input-output representation of linear multivariable systems, Ricerche di Automatica, Vol. 2, no. 1, Jan. 1971.
C. Bonivento andR. Guidorzi,Parametric identification of linear multivariable systems, JACC Preprints, paper no. 5-C6, S. Louis, Aug. 1971.
Author information
Authors and Affiliations
Additional information
This work was supported by CNR (Italian Council of Researches).
Rights and permissions
About this article
Cite this article
Bonivento, C., Guidorzi, R. A note on the transformation from companion to jordan canonical form for multivariable systems. Meccanica 6, 197–203 (1971). https://doi.org/10.1007/BF02128913
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02128913