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Factorization and the Nehari theorem in time-varying systems

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Abstract

The Nehari Theorem and related results on operator interpolation play an important role in modern system theory. These results are embedded in a function-theoretic conceptual framework and therefore restricted to LTI systems. We give a state space oriented extension of the Nehari Theorem to a time-varying system-theoretic setting. In that setting the theorem addresses the issue of measuring the distance between a noncausal bounded I/O operator and the family of causal I/O operators in stable linear systems. The analysis is based on the recent time-domain LQ optimization approach to robust control. The discussion includes a geometrical analysis of stable and antistable invariant subspaces, a short study of certain types of co-prime factorizations of I/O operators in time-varying systems, and a parametrization of all suboptimal solutions.

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Authors and Affiliations

  1. Department of Electrical and Computer Engineering, Northeastern University, 409 Dana Building, 02115, Boston, Massachusetts, USA

    Gilead Tadmor

  2. Department of Electrical Engingeering, McGill University, H3A 2A7, Montréal, Canada

    Madanpal Verma

Authors
  1. Gilead Tadmor
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  2. Madanpal Verma
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Additional information

The research was supported in part by the National Science Foundation under Grant ECS 9108927 and by the U.S. Army Research Office under Contract DAALO3 92 G 0015.

The research was supported by NSERC, Canada.

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Tadmor, G., Verma, M. Factorization and the Nehari theorem in time-varying systems. Math. Control Signal Systems 5, 419–452 (1992). https://doi.org/10.1007/BF02134014

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  • DOI: https://doi.org/10.1007/BF02134014

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