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On the controllability and observability of fractional proportional linear systems

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  • Khizra Bukhsh
  • Awais Younus

Abstract

This paper deals with generalised Caputo fractional proportional linear time-invariant systems in a finite-dimensional space. The Laplace transformation method ensures the analytical solution of the desired fractional linear time-invariant systems. The present article presents the necessary and sufficient conditions for controllability and observability of the generalised Caputo proportional fractional linear time-invariant systems. These two properties can play a more fundamental role in system analysis before controller and observer designs are engaged. Moreover, we have acquired the criterion for generalised Caputo proportional fractional linear time-invariant systems as Kalman rank conditions. Some numerical examples are presented to show the applicability of the paper to demonstrate our findings. Finally, we derive the necessary and sufficient controllability conditions for the generalised Caputo proportional fractional-order nonlinear Chua's electric circuit.

Suggested Citation

  • Khizra Bukhsh & Awais Younus, 2023. "On the controllability and observability of fractional proportional linear systems," International Journal of Systems Science, Taylor & Francis Journals, vol. 54(7), pages 1410-1422, May.
    • Handle: RePEc:taf:tsysxx:v:54:y:2023:i:7:p:1410-1422
    DOI: 10.1080/00207721.2023.2177902
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