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Robust D-stability Analysis of a Class of Interval Fractional Order Systems

Mohsenipour, Reza | 2019

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  1. Type of Document: Ph.D. Dissertation
  2. Language: Farsi
  3. Document No: 51984 (45)
  4. University: Sharif University of Technology
  5. Department: Aerospace Engineering
  6. Advisor(s): Fathi Jegarkandi, Mohsen
  7. Abstract:
  8. Because of advancing fractional calculus and modeling physical phenomena by using fractional calculus more accurately than that by using integer calculus, and also existing uncertainties in models of real world systems, robust stability and performance analysis of fractional order systems are necessary. This thesis deals with the robust -stability analysis of LTI fractional order systems from kind of uncertain typical fractional order systems (UTFOS) and the robust stability analysis of LTI fractional order systems with delays from kind of uncertain retarded type systems (URTS) and uncertain neutral type systems (UNTS) with interval uncertainties. The coefficients of the numerator and the denominator of the transfer functions of these systems are supposed to be real uncertain parameters, and then the robust -stability and the robust stability of the resulted families are investigated. One of the ways for doing this for integer order systems is to use the value set tool that has been recently applied to fractional order systems for studying their robust BIBO stability. In this thesis, this tool is utilized for extending the related results. The novelty of this thesis is presenting necessary and sufficient conditions for the robust -stability analysis of UTFOS of commensurate and incommensurate orders, and the robust stability analysis of URTS and UNTS with multiple time delays. Moreover, using the achieved theorems, fractional order MIMO controllers are designed to control the longitudinal motion of an airplane
  9. Keywords:
  10. Robust Stability ; Fractional Order System ; Value Set ; Linear Time Invarient Systems ; Delayed Systems ; Interval Uncertainty

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