Advances in Difference Equations
Volume 2007 (2007), Article ID 26196, 16 pages
Linear Impulsive Periodic System with Time-Varying Generating Operators on Banach Space
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.
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 -periodic -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 -periodic -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 -periodic -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.