Exponential state estimate of positive systems with time-varying delays: a Lyapunov–Razumikhin approach.

This article focuses on establishing a new approach for obtaining |$\alpha$|-exponential state estimates of positive systems with bounded time-varying delays using a linear Lyapunov–Razumikhin function. It introduces a novel sufficient condition for the exponential boundedness of such systems and proposes two computational methods—one incorporating optimization techniques via linear programming—to determine the factor vector of the state estimate with improved accuracy. Numerical examples demonstrate that the proposed methods yield tighter and more accurate |$\alpha$|-exponential state estimates compared to existing approaches based on Lyapunov–Krasovskii functionals and direct state evaluations. The work highlights the advantages of the linear Lyapunov–Razumikhin function, notably its simpler form without integral terms, which contributes to more precise state bounding in positive time-delay systems.