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Abstract and Applied Analysis
Volume 2014 (2014), Article ID 860378, 7 pages
Research Article

Linearization of Nonautonomous Impulsive System with Nonuniform Exponential Dichotomy

1Department of Mathematics, Zhejiang Normal University, Jinhua, Zhejiang 321004, China
2School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore 639798

Received 1 January 2014; Accepted 22 February 2014; Published 30 March 2014

Academic Editor: Yongli Song

Copyright © 2014 Yongfei Gao et al. 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 gives a version of Hartman-Grobman theorem for the impulsive differential equations. We assume that the linear impulsive system has a nonuniform exponential dichotomy. Under some suitable conditions, we proved that the nonlinear impulsive system is topologically conjugated to its linear system. Indeed, we do construct the topologically equivalent function (the transformation). Moreover, the method to prove the topological conjugacy is quite different from those in previous works (e.g., see Barreira and Valls, 2006).