Construction of lyapunov functions for networks of iISS systems: An explicit solution for a cyclic structure

This paper addresses the problem of constructing Lyapunov functions to establish integral input-to-state stability (iISS) for networks of nonlinear systems. Since the iISS small-gain theorem developed recently has been restricted to interconnection of two subsystems, this paper formulates the problem for a network consisting of more than two iISS subsystems interconnected in a general way. In the case of a cyclic interconnection structure, this paper explicitly shows a solution from which an iISS Lyapunov function of the cyclic network is composed immediately. This paper aims at improving the author´s iISS small-gain technique for deriving a general stability criterion linked directly to a general procedure for explicitly constructing a Lyapunov function for a broader class of iISS networks.