On Asymptotic Stability Criteria for Neutral Differential Equations with Variable Delay

In this study, asymptotic stability criteria are investigated for a class of neutral differential equations with multiple variable delays. The delay terms in the considered equations involve multiple variable delays, which significantly affect the qualitative behavior of the solutions. By constructing an appropriate Lyapunov function and employing some fundamental inequalities together with various estimation techniques, new sufficient conditions guaranteeing the asymptotic stability of the trivial solution are derived. Under general boundedness and continuity assumptions on the coefficients and delay functions, delay-dependent stability criteria are established. The obtained results extend and improve existing stability conditions for neutral systems with a single delay or constant delays reported in the literature. Moreover, illustrative examples are provided to demonstrate the applicability and effectiveness of the proposed criteria.