Small Gain Theorems for Large Scale Systems and Construction of ISS Lyapunov Functions

We consider a network consisting of n interconnected nonlinear subsystems. For each subsystem an ISS Lyapunov function is given that treats the other subsystems as independent inputs. We use a gain matrix 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, we construct a locally Lipschitz continuous ISS Lyapunov function for the entire network by appropriately scaling the individual Lyapunov functions for the subsystems. Key words. Nonlinear systems, input-to-state stability, interconnected systems, large-scale systems, Lipschitz ISS Lyapunov function, small gain condition AMS subject classifications. 93A15, 34D20, 47H07

• Type: Journal
• Year: 2010
• Where: SIAMCO
• Authors: Sergey Dashkovskiy, Björn Sebastian Rüffer, Fabian Wirth
• Keywords: Gain Matrix, ISS Lyapunov Function, SIAMCO 2010, Subsystems