Optimal Control on the Doubly Infinite Time Axis for Well-Posed Linear Systems

Mark Opmeer, Olof Staffans

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Abstract

We study the problem of existence of weak right or left or strong coprime factorizations in H-infinity over the right half-plane of an analytic function defined and uniformly bounded on some right half-plane. We give necessary and sufficient conditions for the existence of such coprime factorizations in terms of an optimal control problem over the doubly infinite continuous-time axis. In particular, we show that an equivalent condition for the existence of a strong coprime factorization is that both the control and the filter algebraic Riccati equation (of an arbitrary well-posed realization) have a solution (in general unbounded and not even densely defined) and that a coupling condition involving these two solutions is satisfied.
Original languageEnglish
Pages (from-to)1985-2015
Number of pages31
JournalSIAM Journal on Control and Optimization
Volume57
Issue number3
Early online date13 Jun 2019
DOIs
Publication statusPublished - 2019

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