New exploration on quasi-uniform stability of fractional-order damped systems with time delay

Abstract This paper explores the quasi-uniform stability (QuS) for damped systems with time delay and the Caputo fractional derivative. Firstly, we establish two new Gronwall integral inequalities (GIIs) with time delay, as well as some corollaries. These inequalities generalize some known GIIs which have been widely applied to the research on differential or integral systems. Next, based on the established inequality, we develop a new criterion on QuS for the discussed systems. Finally, we examine the effectiveness of our condition by providing some numerical examples. Meanwhile, the further analysis shows that our result is less conservative than the one in the existing work.