Small gain theorems for large scale systems and construction of ISS Lyapunov functions

Details Small gain theorems for large scale systems and construction of ISS Lyapunov functions Small gain theorems for large scale systems and construction of ISS Lyapunov functions

2009-01-13

arxiv.org/abs/0901.1842v2

SIAM J. Control Optim. 48 (6):4089-4118, 2010

Mathematics

Optimization and Control

provisionally accepted by SIAM Journal on Control and Optimization

Scientific paper

10.1137/090746483

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.

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