Publication

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).

Research output: Chapter in Book/Report/Conference proceedingChapterAcademicpeer-review

APA

van der Schaft, A. (2017). L2-Gain and the Small-Gain Theorem. In Communications and Control Engineering (pp. 199-211). (Communications and Control Engineering; No. 9783319499918). Springer International Publishing. https://doi.org/10.1007/978-3-319-49992-5_8

Author

van der Schaft, Arjan. / L2-Gain and the Small-Gain Theorem. Communications and Control Engineering. Springer International Publishing, 2017. pp. 199-211 (Communications and Control Engineering; 9783319499918).

Harvard

van der Schaft, A 2017, L2-Gain and the Small-Gain Theorem. in Communications and Control Engineering. Communications and Control Engineering, no. 9783319499918, Springer International Publishing, pp. 199-211. https://doi.org/10.1007/978-3-319-49992-5_8

Standard

L2-Gain and the Small-Gain Theorem. / van der Schaft, Arjan.

Communications and Control Engineering. Springer International Publishing, 2017. p. 199-211 (Communications and Control Engineering; No. 9783319499918).

Research output: Chapter in Book/Report/Conference proceedingChapterAcademicpeer-review

Vancouver

van der Schaft A. L2-Gain and the Small-Gain Theorem. In Communications and Control Engineering. Springer International Publishing. 2017. p. 199-211. (Communications and Control Engineering; 9783319499918). https://doi.org/10.1007/978-3-319-49992-5_8


BibTeX

@inbook{37ff68f1a3c74dd882d27729974894af,
title = "L2-Gain and the Small-Gain Theorem",
abstract = "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",
keywords = "Manifold",
author = "{van der Schaft}, Arjan",
year = "2017",
month = "1",
day = "1",
doi = "10.1007/978-3-319-49992-5_8",
language = "English",
isbn = "978-3-319-49991-8",
series = "Communications and Control Engineering",
publisher = "Springer International Publishing",
number = "9783319499918",
pages = "199--211",
booktitle = "Communications and Control Engineering",

}

RIS

TY - CHAP

T1 - L2-Gain and the Small-Gain Theorem

AU - van der Schaft, Arjan

PY - 2017/1/1

Y1 - 2017/1/1

N2 - 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

AB - 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

KW - Manifold

U2 - 10.1007/978-3-319-49992-5_8

DO - 10.1007/978-3-319-49992-5_8

M3 - Chapter

SN - 978-3-319-49991-8

T3 - Communications and Control Engineering

SP - 199

EP - 211

BT - Communications and Control Engineering

PB - Springer International Publishing

ER -

ID: 111898892