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SIAMCO
2010

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

9 years 25 days ago
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
Sergey Dashkovskiy, Björn Sebastian Rüff
Added 30 Jan 2011
Updated 30 Jan 2011
Type Journal
Year 2010
Where SIAMCO
Authors Sergey Dashkovskiy, Björn Sebastian Rüffer, Fabian Wirth
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