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On the Stable Exact Model Matching and Stable Minimal Design Problems

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Multivariable Control

Abstract

A number of results on the module structure of the set M* of all proper rational vectors which have no poles inside a “forbidden” region Ω of the finite complex plane and which are also contained in a given rational vector space T(s) are surveyed. The structure of the various bases of M* is examined and the notion of a simple basis of M* is introduced. The existence and construction of simple proper and Ω-stable bases of T(s) having minimal MacMillan degree among all other proper bases of T(s) is established. In the light of these concepts and results a number of linear multivariable control algebraic synthesis problems are examined. Thus, necessary and sufficient conditions for the solvability of the “stable exact model matching problem” (SEMMP) are derived and the family of all “proper and stable” solutions to the SEMMP is characterized. Also the minimal design and the stable minimal design problems (MDP)(SMDP) are examined.

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Author information

Authors and Affiliations

  1. Department of Mathematics, Faculty of Sciences Aristotle University of Thessaloniki, Thessaloniki, Greece

    Antonis I. G. Vardulakis

  2. Control Engineering Centre School of Electrical Engineering and Applied Physics, The City University, Northampton Square, London, EC1V 0HB, England

    Nicos Karcanias

Authors
  1. Antonis I. G. Vardulakis
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  2. Nicos Karcanias
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Editor information

Editors and Affiliations

  1. Electrical Engineering Department, University of Patras, Patras, Greece

    Spyros G. Tzafestas

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© 1984 D. Reidel Publishing Company, Dordrecht, Holland

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Vardulakis, A.I.G., Karcanias, N. (1984). On the Stable Exact Model Matching and Stable Minimal Design Problems. In: Tzafestas, S.G. (eds) Multivariable Control. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-6478-5_13

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  • DOI: https://doi.org/10.1007/978-94-009-6478-5_13

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-009-6480-8

  • Online ISBN: 978-94-009-6478-5

  • eBook Packages: Springer Book Archive

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