Hostname: page-component-7dd5485656-k8lnt Total loading time: 0 Render date: 2025-10-31T04:56:15.253Z Has data issue: false hasContentIssue false
  • English
  • Français

Matrices of rational functions

Published online by Cambridge University Press:  17 April 2009

W.A. Coppel
W.A. Coppel
Affiliation:
Department of Mathematics, Institute of Advanced Studies, Australian National University, Canberra, ACT.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

The properties of the degree of a matrix of rational functions are obtained in a simplified way, which enables them to be generalised to matrices whose elements are not necessarily rational functions. On the basis of these results a theory of realisations is developed, which similarly generalises the theory of state space realisations of a matrix of rational functions.

Information

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 11 , Issue 1 , August 1974 , pp. 89 - 113
Copyright
Copyright © Australian Mathematical Society 1974

References

[1]Anderson, B.D.O., “A system theory criterion for positive real matrices”, SIAM J. Control 5 (1967), 171–182.CrossRefGoogle Scholar
[2]Brockett, Roger W., Finite dimensional linear systems (John Wiley and Sons, New York, London, Sydney, Toronto, 1970).Google Scholar
[3]Duffin, R.J. and Hazony, D., “The degree of a rational matrix function”, SIAM J. Appl. Math. 11 (1963), 645–658.Google Scholar
[4]Frobenius, Ferdinand Georg, Gesammelte Abhandlungen, Band II (Springer-Verlag, Berlin, Heidelberg, New York, 1968).Google Scholar
[5]Jacobson, Nathan, Lectures in abstract algebra, Volume II (Van Nostrand, New York, Toronto, London, 1953).Google Scholar
[6]Якубович, В.А. [Jakubovič, V.A.], “Частотная теорема в теории управления” [Frequency theorems in control theory], Sibirsk. Mat. Ž. 14 (1973), 384–420.Google ScholarPubMed
[7]Kalman, R.E., “Irreducible realizations and the degree of a rational matrix”, SIM J. Appl. Math. 13 (1965), 520–541.Google Scholar
[8]MacDuffee, C.C., The theory of matrices, corrected reprint of first edition (Chelsea, New York, 1946).Google Scholar
[9]McMillan, Brockway, “Introduction to formal realizability theory – I”, Bell System Tech. J. 31 (1952), 217–279.Google Scholar
[10]McMillan, Brockway, “Introduction to formal realizability theory – II”, Bell System Tech. J. 31 (1952), 541–600.CrossRefGoogle Scholar
[11]Molinari, B.P., “The stabilizing solution of the algebraic Riccati equation”, SIAM J. Control 11 (1973), 262–271.CrossRefGoogle Scholar
[12]Molinari, B.P., “Equivalence relations for the algebraic Riccati equation”, SIAM J. Control 11 (1973), 272–285.Google Scholar
[13]Popov, V.M., “Hyperstability and optimality of automatic systems with several control functions”, Rev. Roumaine Sci. Tech. Sér. Électrotech. Énergét. 9 (1964), 629–690.Google Scholar
[14]Rosenbrock, H.H., State-space and multivariable theory (Nelson, London, 1970).Google Scholar