Journal of Inequalities and Applications
Volume 2008 (2008), Article ID 563845, 12 pages
Research Article

New LMI-Based Conditions for Quadratic Stabilization of LPV Systems

Wei Xie

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

Received 16 January 2008; Revised 5 August 2008; Accepted 24 November 2008

Academic Editor: Alexander Domoshnitsky

Copyright © 2008 Wei Xie. 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.


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.