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Oscillations in fractional order LTI systems: Harmonic analysis and further results

Siami, M ; Sharif University of Technology | 2013

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  1. Type of Document: Article
  2. DOI: 10.1016/j.sigpro.2012.12.004
  3. Publisher: 2013
  4. Abstract:
  5. This paper studies undamped oscillations generated by marginally stable fractional order linear time invariant (LTI) systems. In this study, an analytical approach is proposed to be used for harmonic analysis of such oscillations in marginally stable commensurate order LTI systems. Also, it is shown that the Q-semi norm of the limit sets for a trajectory of these systems can be analytically determined based on the Q-semi norm of the initial condition, where Q is a specific matrix. Moreover, this result is extended to the wider class of rational order systems. Finally, some numerical examples are presented to demonstrate the use of the paper results
  6. Keywords:
  7. Fractional order system ; Analytical approach ; Fractional order ; Initial conditions ; Limit sets ; Linear time-invariant system ; LTI systems ; Marginal stability ; Numerical example ; Order systems ; Oscillations ; Linear systems ; Harmonic analysis
  8. Source: Signal Processing ; Volume 93, Issue 5 , 2013 , Pages 1243-1250 ; 01651684 (ISSN)
  9. URL: http://www.sciencedirect.com/science/article/pii/S0165168412004422