Advances in Difference Equations
Volume 2007 (2007), Article ID 26196, 16 pages
doi:10.1155/2007/26196
Research Article

Linear Impulsive Periodic System with Time-Varying Generating Operators on Banach Space

JinRong Wang,1 X. Xiang,1,2 and W. Wei2

1Department of Computer, College of Computer Science and Technology, Guizhou University, Guiyang, Guizhou 550025, China
2Department of Mathematics, College of Science, Guizhou University, Guiyang, Guizhou 550025, China

Received 3 May 2007; Accepted 28 August 2007

Academic Editor: Paul W. Eloe

Copyright © 2007 JinRong Wang 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.

Abstract

A class of the linear impulsive periodic system with time-varying generating operators on Banach space is considered. By constructing the impulsive evolution operator, the existence of T0-periodic PC-mild solution for homogeneous linear impulsive periodic system with time-varying generating operators is reduced to the existence of fixed point for a suitable operator. Further the alternative results on T0-periodic PC-mild solution for nonhomogeneous linear impulsive periodic system with time-varying generating operators are established and the relationship between the boundness of solution and the existence of T0-periodic PC-mild solution is shown. The impulsive periodic motion controllers that are robust to parameter drift are designed for a given periodic motion. An example given for demonstration.