Stability Analysis and Stabilization of Fractional‐Order Systems With Distributed Delay

ABSTRACT This paper investigates the stability and stabilization problems of fractional‐order systems with distributed delays (FOSDDs). Firstly, with the frequency sweeping technique and generalized Kalman‐Yakubovi‐Popov (KYP) lemma, a novel stability condition for FOSDDs is proposed. Secondly, based on the proposed stability condition, a robust stability condition for the uncertain FOSDDs with norm‐bounded uncertainties is derived. Thirdly, based on the proposed robust stability condition, a novel stabilization condition for the uncertain FOSDDs with norm‐bounded uncertainties is obtained. Finally, several numerical examples are provided to show the effectiveness of the proposed results. Moreover, in the numerical examples, the comparison of the proposed results with the existing results for FOSDDs is shown to demonstrate that the obtained results are less conservative.