Computing asymptotic gains of large-scale interconnections

This paper considers the problem of verifying stability of large-scale nonlinear dynamical systems. Using a comparison principle approach we present a numerical method for estimating the asymptotic gain characterizing the effect of external disturbances on the stability of a large-scale interconnection. The key contribution is to make use of solely the knowledge of one single trajectory of the comparison system for estimating the behavior of all possible trajectories. It is shown that an asymptotic gain can be obtained from just a single trajectory of a disturbance-free comparison system. The single-trajectory approach leads to a computationally cheap numerical check for the input-to-state practical stability property of a large-scale system.