Abstract
Polynomial Matrix Description of transfer matrices received a great deal of attention during the last decade. This formulation exhibits the finite pole and zero structure generalizing the monovariable case. In the last few years, there has been an increasing interest in factorizations at infinity. The present paper focuses these factorizations, which permits the pointing out of invariant structures under some groups of transformations. The paper is organized as follows. First, left and right Wiener-Hopf factorizations at infinity are presented. Basic properties and some control interpretations are recalled. A characterization of dynamic equivalence is given in terms of Wiener-Hopf factorizations. In the second part we study the Smith Mc Millan factorization at infinity of a transfer function and propose some control interpretations of this factorization. A characterization of the stabilizer of Morse group at (A, B, C) is given for irreducible systems.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
References
WOLOWICH W.A., “Linear multivariable systems”, Springer Verlag, 1974
VERGHESE G., “Infinite frequency, behaviour of generalized dynamical systems”, PhD Thesis, Elect. Eng. Dpt, Stanford University, 1978
FUHRMANN P.A. and WILLEMS J.C., “The factorization indices for rational function matrices”, Integral Equations Oper. Theory, vol. 2, pp. 287–301, 1979
MORSE A.S., “System invariants under feedback and cascade control”, Proc. International Symp., Udine, Springer, 1975
WOLOWICH W.A. and FALB P.L., “Invariants and canonical forms under dynamic compensation”, SIAM J. on Contr. and Opt., vol. 14, pp. 996–1008, 1976
PERNEBO L., “An algebraic theory for the design of controllers for linear multivariable systems”, Parts I and II, IEEE Trans. on Auto. Cont., AC 26, pp. 171–194, 1981
ROSENBROCK H.H., “State space and multivariable theory”, Nelson, London, 1970
PUGH A.C. and RATCLIFFE P.A., “On the zeros and poles of a rational matrix”, Int. J. Control, Vol. 30, pp. 213–226, 1979
VARDULAKIS A.I.G., “On infinite zeros”, Int. J. Control, vol. 32, pp. 849–866, 1980
BHATTACHARYYA S.P., “Frequency domain conditions for disturbance rejection”, IEEE Trans. Auto. Contr., AC 25, pp. 1211–1213, 1980
OWENS D.H., “On structural invariants and the Root-Loci of linear multivariable systems”, Int. J. Contr., vol. 28, pp. 187–196, 1978
FRANCIS B.A., “On totally singular linear quadratic optimal control”, IEEE Trans. Auto. Cont., AC 24, pp. 616–621, 1979
MORSE A.S., “Structural invariants of linear multivariable systems”, SIAM J. Cont. and Opt., vol.11, pp. 446–465, 1973
COMMAULT C. and DION J.M., “Structure at infinity of linear multivariable systems — A geometric approach”, submitted for publication, 1981
WONHAM W.M., “Linear multivariable control: a geometric approach”, (2nd Edition) Springer Verlag, 1979
ANDERSON B.D.O., “A note on transmission zeros of a transfer matrix”, IEEE Trans. Auto. Cont., AC 21, pp. 589–591, 1976
HAUTUS M.L.J. and HEYMANN M., “Linear feedback, an algebraic approach”, SIAM J. Cont. and Opt., Vol. 16, pp. 83–105, 1978
MUNZNER H. and PRATZEL-WOLTERS O., “Minimal bases of polynomial modules, structural indices and Brunovsky transformations”, Int.J.Cont.,vol.30,pp.291–318, 1979
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1982 Springer-Verlag
About this paper
Cite this paper
Dion, J.M., Commault, C. (1982). Some factorizations at infinity of rational matrix functions and their control interpretation. In: Hinrichsen, D., Isidori, A. (eds) Feedback Control of Linear and Nonlinear Systems. Lecture Notes in Control and Information Sciences, vol 39. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0006818
Download citation
DOI: https://doi.org/10.1007/BFb0006818
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-11749-0
Online ISBN: 978-3-540-39479-2
eBook Packages: Springer Book Archive