Small gain theorems for large scale systems and construction of ISS Lyapunov functions - Mathematics > Optimization and ControlReport as inadecuate




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Abstract: We consider interconnections of n nonlinear subsystems in the input-to-statestability ISS framework. For each subsystem an ISS Lyapunov function is giventhat treats the other subsystems as independent inputs. A gain matrix is usedto encode the mutual dependencies of the systems in the network. Under a smallgain assumption on the monotone operator induced by the gain matrix, a locallyLipschitz continuous ISS Lyapunov function is obtained constructively for theentire network by appropriately scaling the individual Lyapunov functions forthe subsystems. The results are obtained in a general formulation of ISS, thecases of summation, maximization and separation with respect to external gainsare obtained as corollaries.



Author: Sergey N. Dashkovskiy, Björn S. Rüffer, Fabian R. Wirth

Source: https://arxiv.org/



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