Factorization and the Nehari theorem in time-varying systems |
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Authors: | Gilead Tadmor Madanpal Verma |
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Affiliation: | (1) Department of Electrical and Computer Engineering, Northeastern University, 409 Dana Building, 02115 Boston, Massachusetts, USA;(2) Department of Electrical Engingeering, McGill University, H3A 2A7 Montréal, Canada |
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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.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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Keywords: | Nehari Theorem Time-varying systems Linear-quadratic optimization Co-prime factorization |
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