Robust Stability and Stabilization Conditions for Fractional-order Systems with Distributed Delays and Polytopic Uncertainties

This paper investigates the robust stability and stabilization conditions for fractional-order systems with distributed delays (FOSDDs) with polytopic uncertainties. To begin with, two robust stability conditions for FOSDDs with polytopic uncertainties are formulated. Subsequently, the state feedback controllers are put forward to robustly stabilize the FOSDDs with polytopic uncertainties. The obtained results are illustrated utilizing linear matrix inequalities (LMIs). Finally, two numerical instances are provided to showcase the effectiveness of the derived conditions.