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Robust stability and stabilization of LTI fractional order systems with polytopic and interval uncertainties

Abooee, A ; Sharif University of Technology

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  1. Type of Document: Article
  2. DOI: 10.1109/IranianCEE.2017.7985437
  3. Abstract:
  4. This paper proposes a novel representation of uncertain LTI fractional order systems based on the state-space model which contains both interval and polytopic uncertainties. First, a set of linear matrix inequalities, which are sufficient conditions, are presented for analyzing the robust stability of the mentioned systems. Then, some sufficient conditions are obtained for designing a feedback gain matrix to tackle the robust stabilization of the considered systems. Note that the concluded conditions of this paper are valid for fractional systems with a given constant derivative order α in 1 ≤ α < 2 and also, can be employed conservatively for α in 0 < α < 1. Finally, through two numerical illustrative examples, the effectiveness and correctness of the given sufficient conditions are verified. © 2017 IEEE
  5. Keywords:
  6. Linear matrix inequality ; LTI fractional order system ; Polytopic uncertainty ; Robust stabilizing controller ; Stability checking ; Algebra ; Closed loop systems ; Linear matrix inequalities ; Matrix algebra ; Robustness (control systems) ; Stabilization ; State space methods ; Fractional-order systems ; Interval uncertainty ; Polytopic uncertainties ; Stabilizing controllers ; System stability
  7. Source: 2017 25th Iranian Conference on Electrical Engineering, ICEE 2017, 2 May 2017 through 4 May 2017 ; 2017 , Pages 2253-2258 ; 9781509059638 (ISBN)
  8. URL: https://ieeexplore.ieee.org/document/7985437