L2-Gain and the Small-Gain Theorem

van der Schaft, A., 1-Jan-2017, Communications and Control Engineering. Springer International Publishing, p. 199-211 13 p. (Communications and Control Engineering; no. 9783319499918).

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  • GainAndTheSmall-GainTheor

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In this chapter, we elaborate on the characterization of finite L2-gain for state space systems, continuing on the general theory of dissipative systems in Chap. 3. Within this framework we revisit the Small-gain theorem and its implications for robustness (Sect. 8.2), and extend the small-gain condition to network systems (Sect. 8.3). Furthermore, we provide an alternative characterization of L2-gain in terms of response to periodic input functions (Sect. 8.4), and in Sect. 8.5 we end by sketching the close relationships to the theory of (integral-)input-to-state stability

Original languageEnglish
Title of host publicationCommunications and Control Engineering
PublisherSpringer International Publishing
Number of pages13
ISBN (Electronic)978-3-319-49992-5
ISBN (Print)978-3-319-49991-8
Publication statusPublished - 1-Jan-2017

Publication series

NameCommunications and Control Engineering
ISSN (Print)0178-5354
ISSN (Electronic)2197-7119


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