Integral input-to-state stability for interconnected discrete-time systems

In this paper, we investigate integral input-to-state stability for interconnected discrete-time systems. The system under consideration contains two subsystems which are connected in a feedback structure. We construct a Lyapunov function for the whole system through the nonlinearly-weighted sum of Lyapunov functions of individual subsystems. We consider two cases in which we assume that one of subsystems is integral input-to-state stable and the other is either input-to-state stable or only integral input-to-state stable