On additive Lyapunov functions and existence of neutral supply rates in acyclic LTI dynamical networks
Andrej Jokić, Ivica Nakić · Repository of Faculty of Mechanical Engineering and Naval Architecture University of Zagreb · 2016
In this paper we are concerned with linear time invariant (LTI) systems which admit a Lyapunov function with a specific additive structure.We prove that if a dynamical network, composed as set of LTI systems interconnected over an acyclic graph, admits an additive quadratic Lyapunov function, then the systems are dissipative with respect to a set of interconnection neutral supply rates (we show that this set is necessarily nonempty), where each supply rate from the set is defined on a single interconnection link in the network.