Equivalent conditions for stabilizability of infinite-dimensional systems with admissible control operators

Birgit Jacob, Hans Zwart

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    16 Citations (Scopus)
    51 Downloads (Pure)

    Abstract

    In this paper we study the optimizability of infinite-dimensional systems with admissible control operators. We show that under a weak condition such a system is optimizable if and only if the system can be split into an exponentially stable subsystem and an unstable subsystem that is exactly controllable in finite time. The state space of the unstable subsystem equals the span of all unstable (generalized) eigenvectors of the original system. This subsystem can be infinite-dimensional. Furthermore, the unstable poles satisfy a summability condition. The state space of the exponentially stable subsystem is given by all vectors for which the action of the original C0 -semigroup is stable.
    Original languageEnglish
    Pages (from-to)1419-1455
    Number of pages37
    JournalSIAM journal on control and optimization
    Volume37
    Issue number5
    DOIs
    Publication statusPublished - 1999

    Keywords

    • Infinite-dimensional systems
    • Controllability
    • Optimizability
    • Stabilizability

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