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A proof for non existence of periodic solutions in time invariant fractional order systems

Tavazoei, M. S ; Sharif University of Technology | 2009

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  1. Type of Document: Article
  2. DOI: 10.1016/j.automatica.2009.04.001
  3. Publisher: 2009
  4. Abstract:
  5. The aim of this note is to highlight one of the basic differences between fractional order and integer order systems. It is analytically shown that a time invariant fractional order system contrary to its integer order counterpart cannot generate exactly periodic signals. As a result, a limit cycle cannot be expected in the solution of these systems. Our investigation is based on Caputo's definition of the fractional order derivative and includes both the commensurate or incommensurate fractional order systems. © 2009 Elsevier Ltd. All rights reserved
  6. Keywords:
  7. Fractional calculus ; Fractional order ; Fractional order derivatives ; Fractional order system ; Fractional-order systems ; Integer order ; Integer-order counterparts ; Limit cycle ; Non-existence ; Periodic signal ; Periodic solution ; Time invariants
  8. Source: Automatica ; Volume 45, Issue 8 , 2009 , Pages 1886-1890 ; 00051098 (ISSN)
  9. URL: https://www.sciencedirect.com/science/article/pii/S0005109809002039