Stability of positive coupled differential-difference equations with unbounded time-varying delays

This paper considers the stability problem of a class of positive coupled differential-difference equations with unbounded time-varying delays. A new method, which is based on upper bounding of the state vector by a decreasing function, is presented to analyze the stability of the system. Different from the existing methods, our method does not use the usual Lyapunov–Krasovskii functional method or the comparison method based on positive systems with constant delays. A new criterion is derived which ensures asymptotic stability of the system with unbounded time-varying delays. A numerical example with simulation results is given to illustrate the stability criterion.