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An efficient numerical algorithm for stability testing of fractional-delay systems

Merrikh Bayat, F ; Sharif University of Technology | 2009

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  1. Type of Document: Article
  2. DOI: 10.1016/j.isatra.2008.10.003
  3. Publisher: 2009
  4. Abstract:
  5. This paper presents a numerical algorithm for BIBO stability testing of a certain class of the so-called fractional-delay systems. The characteristic function of the systems under consideration is a multi-valued function of the Laplace variable s which is defined on a Riemann surface with finite number of Riemann sheets where the origin is a branch point. The stability analysis of such systems is not straightforward because there is no universally applicable analytical method to find the roots of the characteristic equation on the right half-plane of the first Riemann sheet. The proposed method is based on the Rouche's theorem which provides the number of the zeros of a given function in a given simple closed contour. One advantage of the proposed method over previous works is that it gives the number and the location of the unstable poles. The algorithm has a reliable result which is illustrated by several examples. © 2008 ISA
  6. Keywords:
  7. Probability density function ; Analytical methods ; Bibo stabilities ; Branch points ; Characteristic equations ; Characteristic functions ; Delay systems ; Finite numbers ; Fractional delay equation ; Fractional-order system ; Laplace variables ; Numerical algorithm ; Numerical algorithms ; Riemann sheets ; Riemann surfaces ; Rouche's theorems ; Stability analyses ; Stability analysis ; Valued functions ; System stability
  8. Source: ISA Transactions ; Volume 48, Issue 1 , 2009 , Pages 32-37 ; 00190578 (ISSN)
  9. URL: https://www.sciencedirect.com/science/article/abs/pii/S0019057808000670