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

- Jin Rong Wang
^{1}Email author, - X. Xiang
^{1, 2}and - W. Wei
^{2}

**2007**:026196

**DOI: **10.1155/2007/26196

© JinRong Wang et al. 2007

**Received: **3 May 2007

**Accepted: **28 August 2007

**Published: **30 October 2007

## 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 -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.

## Authors’ Affiliations

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