Small gain theorems for large scale systems and construction of ISS Lyapunov functions
S.N. Dashkovskiy, B.S. Rüffer, F.R. Wirth, in: Proc. 51st IEEE Conf. Decis. Control, Maui, Hawaii, USA, 2012, pp. 4165–4170.
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Dashkovskiy, Sergey N.;
Rüffer, Björn S.;
Wirth, Fabian R.
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Abstract
This invited paper is a significantly shortened excerpt of the article S. N. DASHKOVSKIY, B. S. RÜFFER, AND F. R. WIRTH, Small gain theorems for large scale systems and construction of ISS Lyapunov functions, SIAM J. Control Optim., 48 (2010), pp. 4089–4118. We consider interconnections of n nonlinear subsystems in the input-to-state stability (ISS) framework. Foreach 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 individualLyapunov functions for the subsystems.
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Proc. 51st IEEE Conf. Decis. Control
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4165–4170
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Dashkovskiy SN, Rüffer BS, Wirth FR. Small gain theorems for large scale systems and construction of ISS Lyapunov functions. In: Proc. 51st IEEE Conf. Decis. Control. ; 2012:4165–4170.
Dashkovskiy, S. N., Rüffer, B. S., & Wirth, F. R. (2012). Small gain theorems for large scale systems and construction of ISS Lyapunov functions. Proc. 51st IEEE Conf. Decis. Control, 4165–4170.
@inproceedings{Dashkovskiy_Rüffer_Wirth_2012, place={Maui, Hawaii, USA}, title={Small gain theorems for large scale systems and construction of ISS Lyapunov functions}, booktitle={Proc. 51st IEEE Conf. Decis. Control}, author={Dashkovskiy, Sergey N. and Rüffer, Björn S. and Wirth, Fabian R.}, year={2012}, pages={4165–4170} }
Dashkovskiy, Sergey N., Björn S. Rüffer, and Fabian R. Wirth. “Small Gain Theorems for Large Scale Systems and Construction of ISS Lyapunov Functions.” In Proc. 51st IEEE Conf. Decis. Control, 4165–4170. Maui, Hawaii, USA, 2012.
S. N. Dashkovskiy, B. S. Rüffer, and F. R. Wirth, “Small gain theorems for large scale systems and construction of ISS Lyapunov functions,” in Proc. 51st IEEE Conf. Decis. Control, 2012, pp. 4165–4170.
Dashkovskiy, Sergey N., et al. “Small Gain Theorems for Large Scale Systems and Construction of ISS Lyapunov Functions.” Proc. 51st IEEE Conf. Decis. Control, 2012, pp. 4165–4170.
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