On Controllability of Networked Higher Dimensional Impulsive Systems

Bulletin of the Iranian Mathematical Society (2021)Cite this article

Abstract

This article proposes various sufficient controllability criteria for a class of networked higher dimensional systems under the influence of impulses exhibited by their state functions. The conditions obtained are characterised in terms of impulse matrices, inner coupling matrix, network topology and the system matrices. It is demonstrated that Kalman’s rank condition and Popov–Belevitch–Hautus (PBH)-rank condition are just sufficient conditions for the controllability of these systems, but not necessary unlike as that of the networked systems without impulses. Various numerical examples are provided to validate the theoretical results. Further, the control function and controlled trajectory are plotted for the systems considered, that helps to estimate the cost of controller.

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Acknowledgements

Authors are grateful to the reviewers and editor-in-chief for their suggestions and comments that helped in the improvement of this article.

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Affiliations

  1. Department of Mathematics, Sri H. D. Devegowda Government First Grade College, Paduvalahippe P. O., Hassan, 573211, India

    Vijayakumar S. Muni

  2. Department of Mathematics, Indian Institute of Space Science and Technology, Valiamala P.O., Thiruvananthapuram, 695547, India

    Raju K. George

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  1. Vijayakumar S. Muni
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  2. Raju K. George
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Correspondence to Vijayakumar S. Muni.

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Muni, V.S., George, R.K. On Controllability of Networked Higher Dimensional Impulsive Systems. Bull. Iran. Math. Soc. (2021). https://doi.org/10.1007/s41980-020-00481-8

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Keywords

  • Impulsive systems
  • Controllability
  • Complex networks

Mathematics Subject Classification

  • 34A37
  • 93B05
  • 05C82