LMI stability conditions and stabilization of fractional-order systems with polytopic and two-norm bounded uncertainties for fractional-order \(\alpha\): the \(1 < \alpha < 2\) case.

*(English)*Zbl 1401.93165Summary: This article addresses the problem of robust stability and stabilization for linear fractional-order system with polytopic and two-norm bounded uncertainties, and focuses particularly on the case of a fractional order \(\alpha\) such that \(1 < \alpha < 2\). First, the robust asymptotical stable condition is presented. Second, the design method of the state feedback controller for asymptotically stabilizing such uncertain fractional order systems is derived. In the proposed approach, linear matrix inequalities formalism is used to check and design. Lastly, two simulation examples are given to validate the proposed theoretical results.

##### MSC:

93D09 | Robust stability |

93D21 | Adaptive or robust stabilization |

93D20 | Asymptotic stability in control theory |

93C05 | Linear systems in control theory |

93C41 | Control/observation systems with incomplete information |

93B52 | Feedback control |

34A08 | Fractional ordinary differential equations and fractional differential inclusions |

##### Keywords:

LTI fractional-order system; polytopic uncertainty; two-norm bounded uncertainty; stability condition; stabilization
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\textit{S. Li}, Comput. Appl. Math. 37, No. 4, 5000--5012 (2018; Zbl 1401.93165)

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