Periodic behavior of locally stabilizing saturated linear controllers for the discrete-time double integrator

Tao Yang, Antonie Arij Stoorvogel, Xu Wang, Ali Saberi

    Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

    2 Citations (Scopus)

    Abstract

    The main contribution of this paper is to point out the vast difference between a discrete-time double integrator subject to actuator saturation and a continuous-time double integrator subject to actuator saturation. In continuous-time, any linear state feedback control law which locally stabilizes the double integrator, also globally stabilizes the double integrator in the presence of actuator saturation. In discrete-time, the equivalent of the double integrator has intrinsically different behavior. Some linear feedbacks which locally stabilize the double integrator, also globally stabilize the double integrator in the presence of actuator saturation. However, other linear feedbacks which locally stabilize the double integrator, do not globally stabilize the double integrator in the presence of actuator saturation. We classify a class of linear feedback laws which achieve local stability but also yield nonzero periodic solutions in the presence of actuator saturation and therefore cannot achieve global asymptotic stability.
    Original languageUndefined
    Title of host publicationProceedings 4th IFAC Symposium on System, Structure and Control
    EditorsL. Jetto
    Place of PublicationLaxenburg, Austria
    PublisherIFAC
    Pages237-241
    Number of pages5
    ISBN (Print)1474-6670
    DOIs
    Publication statusPublished - Sep 2010

    Publication series

    Name
    PublisherIFAC
    ISSN (Print)1474-6670

    Keywords

    • METIS-276300
    • Systems Subject to Constraints
    • EWI-19342
    • Constrained Control
    • IR-75727
    • Nonlinear Systems

    Cite this

    Yang, T., Stoorvogel, A. A., Wang, X., & Saberi, A. (2010). Periodic behavior of locally stabilizing saturated linear controllers for the discrete-time double integrator. In L. Jetto (Ed.), Proceedings 4th IFAC Symposium on System, Structure and Control (pp. 237-241). Laxenburg, Austria: IFAC. https://doi.org/10.3182/20100915-3-IT-2017.00058