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New LMI-Based Conditions for Quadratic Stabilization of LPV Systems

Abstract

This paper is concerned with quadratic stabilization problem of linear parameter varying (LPV) systems, where arbitrary time-varying dependent parameters are belonging to a polytope. It provides improved linear matrix inequality- (LMI-) based conditions to compute a gain-scheduling state-feedback gain that makes closed-loop system quadratically stable. The proposed conditions, based on the philosophy of Pólya's theorem, are written as a sequence of progressively less and less conservative LMI. More importantly, by adding an additional decision variable, at each step, these new conditions provide less conservative or at least the same results than previous methods in the literature.

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Correspondence to Wei Xie.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Xie, W. New LMI-Based Conditions for Quadratic Stabilization of LPV Systems. J Inequal Appl 2008, 563845 (2008). https://doi.org/10.1155/2008/563845

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  • DOI: https://doi.org/10.1155/2008/563845

Keywords

  • Decision Variable
  • Previous Method
  • Stabilization Problem
  • Linear Matrix Inequality
  • Linear Matrix