Scalable Input-to-State Stability of Nonlinear Interconnected Systems

This article investigates the scalable input-to-state stability (sISS) property of networks of interconnected systems using the local Lyapunov functions of the individual systems or agents that compose the network. Ensuring sISS of the network prevents the amplification of disturbances through the network, provides uniform transient performance with respect to the number of interconnected systems, and enables network scalability. Our first contribution is to provide sufficient conditions for sISS of networks using sISS vector Lyapunov functions. These sufficient conditions are given in terms of the Lyapunov functions of the agents. We use vector Lyapunov functions, the comparison lemma, and contraction analysis to prove the result. Our second contribution provides conditions for sISS of weakly coupled interconnected systems. This result allows us to study the sISS of exponentially stable systems interconnected by weak coupling links. We illustrate the application of the results in four examples.