Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article Linear Impulsive Periodic System with Time-Varying Generating Operators on Banach Space | Hindawi Publishing Corporation Advances in Difference Equations Volume 2007 Article ID 26196 16 pages doi 2007 26196 Research Article Linear Impulsive Periodic System with Time-Varying Generating Operators on Banach Space JinRong Wang X. Xiang and W. Wei Received 3 May 2007 Accepted 28 August 2007 Recommended by Paul W. Eloe 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 is given for demonstration. 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. 1. Introduction It is well known that periodic motion is a very important and special phenomenon not only in natural science but also in social science. The periodic solution theory of dynamic equations has been developed over the last decades. We refer the readers to 1-11 for infinite dimensional cases to 12-15 for finite dimensional cases. Especially there are many results of periodic solutions such as existence the relationship between bounded solutions and periodic solutions stability and robustness for non-autonomous impulsive periodic system on finite dimensional spaces see 12 14 15 . There .
