Small-Gain and Passivity for Input–Output Maps

van der Schaft, Arjan

doi:10.1007/978-3-319-49992-5_2

Arjan van der Schaft⁶

Part of the book series: Communications and Control Engineering ((CCE))

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Abstract

In this chapter we give the basic versions of the classical small-gain (Sect. 2.1) and passivity theorems (Sect. 2.2) in the study of closed-loop stability.

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Notes

1.
A function \(\gamma : \mathbbm {R}^+ \rightarrow \mathbbm {R}^+\) is of class \(\mathcal{K}\) (denoted \(\gamma \in \mathcal{K}\)) if it is zero at zero, strictly increasing and continuous.

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Johann Bernoulli Institute for Mathematics and Computer Science, University of Groningen, Groningen, The Netherlands
Arjan van der Schaft

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Arjan van der Schaft
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Correspondence to Arjan van der Schaft .

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van der Schaft, A. (2017). Small-Gain and Passivity for Input–Output Maps. In: L2-Gain and Passivity Techniques in Nonlinear Control. Communications and Control Engineering. Springer, Cham. https://doi.org/10.1007/978-3-319-49992-5_2

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DOI: https://doi.org/10.1007/978-3-319-49992-5_2
Published: 06 December 2016
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-49991-8
Online ISBN: 978-3-319-49992-5
eBook Packages: EngineeringEngineering (R0)

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