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Robust D-stability test of LTI general fractional order control systems

Mohsenipour, R ; Sharif University of Technology | 2020

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  1. Type of Document: Article
  2. DOI: 10.1109/JAS.2020.1003159
  3. Publisher: Institute of Electrical and Electronics Engineers Inc , 2020
  4. Abstract:
  5. This work deals with the robust D-stability test of linear time-invariant ( LTI ) general fractional order control systems in a closed loop where the system and - or the controller may be of fractional order. The concept of general implies that the characteristic equation of the LTI closed loop control system may be of both commensurate and non-commensurate orders, both the coefficients and the orders of the characteristic equation may be nonlinear functions of uncertain parameters, and the coefficients may be complex numbers. Some new specific areas for the roots of the characteristic equation are found so that they reduce the computational burden of testing the robust D-stability. Based on the value set of the characteristic equation, a necessary and sufficient condition for testing the robust D-stability of these systems is derived. Moreover, in the case that the coefficients are linear functions of the uncertain parameters and the orders do not have any uncertainties, the condition is adjusted for further computational burden reduction. Various numerical examples are given to illustrate the merits of the achieved theorems. © 2014 Chinese Association of Automation
  6. Keywords:
  7. Computation theory ; Control system stability ; Control systems ; Linear control systems ; Nonlinear equations ; Stability ; Uncertainty analysis ; Characteristic equation ; Computational burden ; Fractional order control system ; Linear functions ; Linear time invariant ; Nonlinear functions ; Robust-D-stability ; Uncertain parameters ; Closed loop control systems
  8. Source: IEEE/CAA Journal of Automatica Sinica ; Volume 7, Issue 3 , May , 2020 , Pages 853-864
  9. URL: https://ieeexplore.ieee.org/document/9080622