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IMA Journal of Mathematical Control and Information Advance Access published online on November 17, 2006
IMA Journal of Mathematical Control and Information, doi:10.1093/imamci/dnl033
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© The author 2006. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.
Received June 14, 2006
Accepted October 2, 2006

Article

Decentralized dynamic pole assignment with low-order compensators

J. Leventides 1 and N. Karcanias 2 *

1 Department of Economics, University of Athens, Pesmazoglou 8, Athens, Greece
2 Control Engineering Centre, School of Engineering and Mathematical Sciences, City University, Northampton Square London EC1V OHB, UK

* To whom correspondence should be addressed.
N. Karcanias, E-mail: n.karcanias{at}city.ac.uk


  Abstract

The problem of arbitrary pole placement via dynamic decentralized output feedback is studied for minimal systems described by a proper transfer function matrix P(s) Rm x p(s) (m = {sum} mi and p = {sum} pi), with McMillan degree n. The family of controllers to be used includes those decentralized controllers with {kappa} channels whose ith channel has maximum observability index at most di. The method presented here is based on asymptotic linearization around a decentralized degenerate compensator of the pole placement map related to the problem. It is shown that the method works generically when m +p > n, where m + = min{di(pi + mi - 1) + mi}, i = 1, ..., {kappa}, and the smallest di of the compensator of the ith channel is the integral part of (n - pmi)/p(pi + mi - 1).

Keywords: decentralized control; control theory; algebro-geometric methods; linear systems.
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