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  • Research Article
  • Open Access

New LMI-Based Conditions for Quadratic Stabilization of LPV Systems

Journal of Inequalities and Applications20082008:563845

  • Received: 16 January 2008
  • Accepted: 24 November 2008
  • Published:


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.


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

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Authors’ Affiliations

College of Automation Science and Technology, South China University of Technology, Guangzhou, 510641, China


© Wei Xie. 2008

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.