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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 1401.93165
Summary: 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
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