LMI-based gain scheduled controller synthesis for a class of linear parameter varying systems

Brian D O Anderson, Alexander Lanzon, Jan Bendtsen

    Research output: Chapter in Book/Report/Conference proceedingChapter


    This paper presents a novel method for constructing controllers for a class of single-input multiple-output (SIMO) linear parameter varying (LPV) systems. This class of systems encompasses many physical systems, in particular systems where individual components vary with time, and is therefore of significant practical relevance to control designers. The control design presented in this paper has the properties that the system matrix of the closed loop is multi-affine in the various scalar parameters, and that the resulting controller ensures a certain degree of stability for the closed loop even when the parameters are varying, with the degree of stability related directly to a bound on the average rate of allowable parameter variations. Thus, if knowledge of the parameter variations is available, the conservativeness of the design can be kept at a minimum. The construction of the controller is formulated as a standard linear time-invariant (LTI) design combined with a set of linear matrix inequalities, which can be solved efficiently with software tools. The design procedure is illustrated by a numerical example. © Springer-Verlag Berlin Heidelberg 2006.
    Original languageEnglish
    Title of host publicationLecture Notes in Control and Information Sciences|Lect. Notes Control Inf. Sci.
    Place of PublicationBerlin, Germany
    PublisherSpringer Nature
    Number of pages22
    Publication statusPublished - 16 Mar 2006


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