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

Authors: Sergey N. Dashkovskiy, Björn S. Rüffer, and Fabian R. WirthAuthors Info & Affiliations

https://doi.org/10.1137/090746483

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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.

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Information & Authors

Information

Published In

cover image SIAM Journal on Control and Optimization

SIAM Journal on Control and Optimization

Volume 48 • Issue 6 • January 2010

Pages: 4089 - 4118

DOI: 10.1137/090746483

ISSN (online): 1095-7138

Copyright

Copyright © 2010 Society for Industrial and Applied Mathematics.

History

Submitted: 14 January 2009

Accepted: 24 March 2010

Published online: 12 May 2010

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Keywords

Authors

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Sergey N. Dashkovskiy

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Björn S. Rüffer

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Fabian R. Wirth

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