Decentralized stabilization of linear time invariant systems subject to actuator saturation

Antonie Arij Stoorvogel, Ali Saberi, Ciprian Deliu, C. Deliu, Peddapullaiah Sannuti

    Research output: Chapter in Book/Report/Conference proceedingChapterAcademicpeer-review

    215 Citations (Scopus)
    66 Downloads (Pure)

    Abstract

    We are concerned here with the stabilization of a linear time invariant system subject to actuator saturation via decentralized control while using linear time invariant dynamic controllers. When there exists no actuator saturation, i.e. when we consider just linear time invariant systems, it is known that global stabilization can be done via decentralized control while using linear time invariant dynamic controllers only if the so-called decentralized fixed modes of it are all in the open left half complex plane. On the other hand, it is known that for linear time invariant systems subject to actuator saturation, semi-global stabilization can be done via centralized control while using linear time invariant dynamic controllers if and only if the open-loop poles of the linearized model of the given system are in the closed left half complex plane. This chapter establishes that the necessary conditions for semi-global stabilization of linear time invariant systems subject to actuator saturation via decentralized control while using linear time invariant dynamic controllers, are indeed the above two conditions, namely (a) the decentralized fixed modes of the linearized model of the given system are in the open left half complex plane, and (b) the open-loop poles of the linearized model of the given system are in the closed left half complex plane. We conjecture that these two conditions are also sufficient in general. We prove the sufficiency for the case when the linearized model of the given system is open-loop conditionally stable with eigenvalues on the imaginary axis being distinct. Proving the sufficiency is still an open problem for the case when the linearized model of the given system has repeated eigenvalues on the imaginary axis.
    Original languageUndefined
    Title of host publicationAdvanced strategies in control systems with input and output constraints
    EditorsS. Tarbouriech, G. Garcia, A.H. Glattfelder
    Place of PublicationLondon
    PublisherSpringer
    Pages397-419
    Number of pages23
    ISBN (Print)978-3-540-37009-3
    DOIs
    Publication statusPublished - 2007

    Publication series

    NameLecture Notes in Control and Information Sciences
    PublisherSpringer Verlag
    Number06472/346
    Volume346
    ISSN (Print)1610-7411

    Keywords

    • METIS-241653
    • MSC-93A14
    • IR-64061
    • EWI-10024

    Cite this

    Stoorvogel, A. A., Saberi, A., Deliu, C., Deliu, C., & Sannuti, P. (2007). Decentralized stabilization of linear time invariant systems subject to actuator saturation. In S. Tarbouriech, G. Garcia, & A. H. Glattfelder (Eds.), Advanced strategies in control systems with input and output constraints (pp. 397-419). (Lecture Notes in Control and Information Sciences; Vol. 346, No. 06472/346). London: Springer. https://doi.org/10.1007/BF00750641, https://doi.org/10.1007/978-3-540-37010-9_14