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IMA Journal of Mathematical Control and Information Advance Access originally published online on November 17, 2006
IMA Journal of Mathematical Control and Information 2007 24(3):395-410; 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.

Decentralized dynamic pole assignment with low-order compensators

J. Leventides

Department of Economics, University of Athens, Pesmazoglou 8, Athens, Greece

N. Karcanias{dagger}

Control Engineering Centre, School of Engineering and Mathematical Sciences, City University, Northampton Square London EC1V OHB, UK

{dagger} Email: n.karcanias{at}city.ac.uk

Received on June 14, 2006; Accepted on October 2, 2006

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) isin 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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