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Volume 7 Issue 3
Apr.  2020

IEEE/CAA Journal of Automatica Sinica

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Article Navigation >  IEEE/CAA Journal of Automatica Sinica  > 2020  >  7(3): 853-864
Reza Mohsenipour and Xinzhi Liu, "Robust D-Stability Test of LTI General Fractional Order Control Systems," IEEE/CAA J. Autom. Sinica, vol. 7, no. 3, pp. 853-864, May 2020. doi: 10.1109/JAS.2020.1003159
Citation: Reza Mohsenipour and Xinzhi Liu, "Robust D-Stability Test of LTI General Fractional Order Control Systems," IEEE/CAA J. Autom. Sinica, vol. 7, no. 3, pp. 853-864, May 2020. doi: 10.1109/JAS.2020.1003159
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Robust D-Stability Test of LTI General Fractional Order Control Systems

doi: 10.1109/JAS.2020.1003159
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    Abstract
  • 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.

     

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    Highlights

    • Investigating the robust D-stability of LTI general fractional order control systems.
    • Parametric uncertainties may exist in anywhere of the system model.
    • Presenting areas for the poles to reduce the computational burden.
    • Introducing a necessary and sufficient condition.
    • Checking the condition by a simple and efficient graphical method.

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