Diagonal Lyapunov–Krasovskii functionals for discrete-time positive systems with delay

•Conditions for diagonal Lyapunov–Krasovskii functional existence are given.•The connection between diagonal L–K functionals and absolute stability is shown.•The previous facts are extended to nonlinear and switched systems.

We consider the existence of diagonal Lyapunov–Krasovskii (L–K) functionals for positive discrete-time systems subject to time-delay. In particular, we show that the existence of a diagonal functional is necessary and sufficient for delay-independent stability of a positive linear time-delay system. We extend this result and provide conditions for the existence of diagonal L–K functionals for classes of nonlinear positive time-delay systems, which are not necessarily order preserving. We also describe sufficient conditions for the existence of common diagonal L–K functionals for switched positive systems subject to time-delay.