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

Advances in Difference Equations volume 2007, Article number: 026196 (2007) Cite this article

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.

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Authors and Affiliations

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

    Jin Rong Wang & X. Xiang

  2. Department of Mathematics, College of Science, Guizhou University, Guiyang, Guizhou, 550025, China

    X. Xiang & W. Wei

Authors
  1. Jin Rong Wang
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  2. X. Xiang
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  3. W. Wei
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Correspondence to Jin Rong Wang.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Wang, J.R., Xiang, X. & Wei, W. Linear Impulsive Periodic System with Time-Varying Generating Operators on Banach Space. Adv Differ Equ 2007, 026196 (2007). https://doi.org/10.1155/2007/26196

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Keywords

  • Differential Equation
  • Partial Differential Equation
  • Ordinary Differential Equation
  • Functional Analysis
  • Functional Equation