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IMA Journal of Mathematical Control and Information 2005 22(1):12-25; doi:10.1093/imamci/dni002
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© Institute of Mathematics and its Applications 2005; all rights reserved. For permissions please email: journals.permissions@oupjournals.org

On the computation and parametrization of proper denominator assigning compensators for strictly proper plants

E. N. Antoniou * and A. I. G. Vardulakis §

Department of Mathematics, Aristotle University of Thessaloniki, 54006 - Thessaloniki, Greece  *

Given a right coprime MFD of a strictly proper plant P(s) = NR(s) DR(s)–1 with DR(s) column proper a simple numerical algorithm is derived for the computation of all polynomial solutions [XL(s), YL(s)] of the polynomial matrix Diophantine equation XL(s) DR(s) + YL(s) NR(s) = DC(s) which give rise to the class {Phi} (P, DC) of proper compensators C(s) colone XL(s)–1 YL(s) that when employed in a unity feedback loop, result in closed-loop systems S(P, C) with a desired denominator DC(s). The parametrization of the proper compensators C(s) {Phi}(P, DC) is obtained and the number of independent parameters in the parametrization is given.

Keywords: linear multivariable control; coprime factorizations; diophantine euqations.

Received on 1 August 2003.

* Corresponding author. Email: antoniou{at}math.auth.gr

§ Email: avardula{at}auth.gr


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