Construction of Lyapunov-Krasovskii functionals for interconnection of retarded dynamic and static systems via a small-gain condition

This paper addresses the problem of constructing Lyapunov-Krasovskii functionals for verifying integral input-to-state stability(iISS) and input-to-state stability(ISS) of time-delay nonlinear systems. Based on decomposition of a time-delay system into a dynamic component (a functional differential equation) and static components (functional algebraic equations), this paper develops an iISS small-gain theorem for the interconnection of these components to assess the stability of the overall time-delay system. Both discrete and distributed delays can be involved in the dynamic and the static components. The result can be considered as a counterpart of the author's previous work which only deals with dynamic components. For the construction of Lyapunov-Krasovskii functionals, this paper introduces a new technique which differs from the one employed in the dynamic case.