Small gain theorems for large scale systems and construction of ISS Lyapunov functions
Abstract
We consider interconnections of n nonlinear subsystems in the input-to-state stability (ISS) framework. For each subsystem an ISS Lyapunov function is given that treats the other subsystems as independent inputs. A gain matrix is used to encode the mutual dependencies of the systems in the network. Under a small gain assumption on the monotone operator induced by the gain matrix, a locally Lipschitz continuous ISS Lyapunov function is obtained constructively for the entire network by appropriately scaling the individual Lyapunov functions for the subsystems. The results are obtained in a general formulation of ISS, the cases of summation, maximization and separation with respect to external gains are obtained as corollaries.
Keywords
Cite
@article{arxiv.0901.1842,
title = {Small gain theorems for large scale systems and construction of ISS Lyapunov functions},
author = {Sergey N. Dashkovskiy and Björn S. Rüffer and Fabian R. Wirth},
journal= {arXiv preprint arXiv:0901.1842},
year = {2010}
}
Comments
provisionally accepted by SIAM Journal on Control and Optimization