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Instability and Unboundedness Analysis for Impulsive Differential Systems with Applications to Lurie Control Systems

  • Xiaodi Li
  • Wu-Hua Chen
  • Wei Xing Zheng
  • Qing-guo Wang
Regular Papers Control Theory and Applications

Abstract

The present paper is dealt with the problem of the instability and unboundedness of impulsive differential systems. Numerous impulsive control systems were reported in the literature. The existing results give sufficient conditions for stability or boundedness of the system. If a system fails such conditions, it might be stable or unstable, bounded or unbounded. The most dangerous among these possible cases are unstable and unbounded ones. To our best knowledge, no criterion is available now to check these two cases. Thus, this paper presents some sufficient conditions on instability and unboundedness of impulsive systems, specializes them to Lurie control systems, and validates them with three illustrative examples.

Keywords

Comparison method impulsive differential systems (IDSs) instability Lurie control systems unboundedness 

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Copyright information

© Institute of Control, Robotics and Systems and The Korean Institute of Electrical Engineers and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Xiaodi Li
    • 1
  • Wu-Hua Chen
    • 2
  • Wei Xing Zheng
    • 3
  • Qing-guo Wang
    • 4
  1. 1.School of Mathematics and StatisticsShandong Normal UniversityJi’nanP. R. China
  2. 2.College of Mathematics and Information ScienceGuangxi UniversityNanning, GuangxiP. R. China
  3. 3.School of Computing, Engineering and MathematicsWestern Sydney UniversitySydneyAustralia
  4. 4.Institute for Intelligent SystemsUniversity of JohannesburgJohannesburgSouth Africa

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