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On Maximal Gains Guaranteeing a Small-Gain Condition

Authors: Roman Geiselhart; Fabian Wirth;

On Maximal Gains Guaranteeing a Small-Gain Condition

Abstract

In the analysis of large-scale interconnected systems, small-gain conditions may be used to derive stability properties of the overall system. This paper investigates the question of how large several gains may be chosen while still satisfying a small-gain condition, if a subset of the gains is fixed. In particular, the cases of summation of linear gains and maximization of gains lead to computable solutions. As an application, we consider the interconnection of a large-scale system with a communication network to be designed. To this end a small-gain theorem in the context of hybrid systems for the interconnection of input-to-state stable and globally pre-stable (pre-GS) subsystems is derived. The pre-GS subsystems model data channels. The construction methods then give gain bounds for the data channels guaranteeing stability of the overall system.

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Powered by OpenAIRE graph
citations
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
9
Average
Average
Top 10%