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 of estimating the asymptotic gain characterizing the effect of external disturbances on the stability of a large-scale interconnection. The unique idea 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 implementation with which we can numerically check whether or not a large-scale system is input-to-state practically stable.

• Type: Journal
• Year: 2010
• Where: CDC
• Authors: Björn Rüffer, Hiroshi Ito, Peter M. Dower
• Keywords: CDC 2010, Control Systems, External Disturbances, Numerical Method, Principle Approach