A refined allowable delay set for stability analysis of linear systems with a sinusoidal delay

ABSTRACT This paper investigates the stability issues of linear systems with a sinusoidal delay, utilizing a refined switching allowable delay set (ADS) derived from the delay‐splitting technique (DST). The delay function is divided into multiple segments and defines their respective value ranges using the DST. By accurately calculating the delay derivatives at each segment point, a refined ADS with a tighter boundary condition is established. Based on this ADS, a stability criterion specifically for linear systems with sinusoidal delays is introduced, demonstrating a significant reduction in conservativeness. Additionally, an improved DST‐based Lyapunov–Krasovskii functional (LKF) is proposed. Compared to similar LKFs reported in the literature, our approach imposes more relaxed constraints, further reducing the conservativeness of the results. Finally, the validity and applicability of our proposed approaches are verified through two extensively researched numerical examples.