Distributed Stability Conditions for Interconnected LTI Systems Based on Differential Interconnection Neutral Functions

In this paper we are concerned with stability of interconnected linear time invariant systems. It is shown that stability conditions involving specifically structured Lyapunov function candidates can be decomposed to a set of local and coupled stability-related conditions, without introducing any additional conservatism. Specific feature of the considered Lyapunov functions is that they include (higher order) time derivatives of the state vector. Decomposition of stability conditions is based on the notion of differential interconnection neutral functions, which are conceptually related to interconnection neutral supply functions from the theory of dissipative dynamical systems.