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Limits of generalized state space systems under proportional and derivative feedback

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Abstract

In this paper we study the high-gain feedback classification problem for generalized state space systems. We solve this problem for proportional and derivative feedback transformations of regularizable systems, i.e., we give necessary and sufficient conditions for a regularizable system to be a limit of a given system under high-gain proportional and derivative feedback. We also derive a new complete set of invariants for proportional feedback equivalence and specify a set of necessary conditions for a system to be the limit of another system under these feedback transformations. The necessary conditions are sufficient for arbitrary state space systems and for controllable singular systems.

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Authors and Affiliations

  1. Institut für Dynamische Systeme, Universität Bremen, D-28344, Bremen, Germany

    D. Hinrichsen

  2. Department of Mathematical Sciences, Portland State University, 97207-0751, Portland, Oregon, USA

    J. O'Halloran

Authors
  1. D. Hinrichsen
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  2. J. O'Halloran
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Additional information

The second author's work on this paper was partially supported by a grant from the National Science Foundation. The support from the University of Bremen is also gratefully acknowledged.

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Hinrichsen, D., O'Halloran, J. Limits of generalized state space systems under proportional and derivative feedback. Math. Control Signal Systems 10, 97–124 (1997). https://doi.org/10.1007/BF01213382

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  • DOI: https://doi.org/10.1007/BF01213382

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