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Robust stability analysis of distributed-order linear time-invariant systems with uncertain order weight functions and uncertain dynamic matrices

Taghavian, H ; Sharif University of Technology

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  1. Type of Document: Article
  2. DOI: 10.1115/1.4037268
  3. Abstract:
  4. Bounded-input bounded-output (BIBO) stability of distributed-order linear time-invariant (LTI) systems with uncertain order weight functions and uncertain dynamic matrices is investigated in this paper. The order weight function in these uncertain systems is assumed to be totally unknown lying between two known positive bounds. First, some properties of stability boundaries of fractional distributed-order systems with respect to location of eigenvalues of dynamic matrix are proved. Then, on the basis of these properties, it is shown that the stability boundary of distributed-order systems with the aforementioned uncertain order weight functions is located in a certain region on the complex plane defined by the upper and lower bounds of the order weight function. Thereby, sufficient conditions are obtained to ensure robust stability in distributed-order LTI systems with uncertain order weight functions and uncertain dynamic matrices. Numerical examples are presented to verify the obtained results. © 2017 by ASME
  5. Keywords:
  6. Eigenvalues and eigenfunctions ; Invariance ; Linear systems ; Matrix algebra ; Stability ; Time varying control systems ; Bounded input bounded output stabilities ; Linear time invariant systems ; Linear time-invariant system ; Robust stability analysis ; Stability boundaries ; Uncertain dynamics ; Upper and lower bounds ; Weight functions ; System stability
  7. Source: Journal of Dynamic Systems, Measurement and Control, Transactions of the ASME ; Volume 139, Issue 12 , 2017 ; 00220434 (ISSN)
  8. URL: http://dynamicsystems.asmedigitalcollection.asme.org/article.aspx?articleid=2644725