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

MR Opmeer, Olof Staffans

    Research output: Contribution to journalArticleScientificpeer-review


    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 languageUndefined/Unknown
    Pages (from-to)1985–2015
    Number of pages31
    JournalSIAM Journal on Control and Optimization
    Issue number3
    Publication statusPublished - 2019
    MoE publication typeA1 Journal article-refereed


    • Riccati equation
    • linear quadratic optimal control
    • infinite-dimensional system
    • coprime factorization
    • input-output stabilization
    • state feedback

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