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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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