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

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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Correspondence to Jin Rong Wang.

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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