(N, ε) stability analysis of nonlinear systems using universal learning networks

Kotaro Hirasawa; Jinglu Hu; Junichi Murata

doi:10.3182/20020721-6-es-1901.00693

(N, ε) stability analysis of nonlinear systems using universal learning networks

Kotaro Hirasawa, Jinglu Hu, Junichi Murata

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Abstract

This paper proposes a stability analysis method based on the higher order derivatives of ULNs. In the proposed method, the following are proposed. Firstly, if the absolute values of the first order derivatives of any coordinates of the original trajectory with respect to any initial disturbances approach zero at time infinity, then the trajectory is locally asymptotically stable. Secondly, the (n, ε) locally asymptotically stable region, where asymptotical stability is secured approximately, is obtained by neglecting the higher order derivatives until nth order with e approximation.

Original language	English
Title of host publication	IFAC Proceedings Volumes (IFAC-PapersOnline)
Editors	Gabriel Ferrate, Eduardo F. Camacho, Luis Basanez, Juan. A. de la Puente
Publisher	IFAC Secretariat
Pages	241-246
Number of pages	6
Edition	1
ISBN (Print)	9783902661746
DOIs	https://doi.org/10.3182/20020721-6-es-1901.00693
Publication status	Published - 2002
Externally published	Yes
Event	15th World Congress of the International Federation of Automatic Control, 2002 - Barcelona, Spain Duration: 2002 Jul 21 → 2002 Jul 26

Publication series

Name	IFAC Proceedings Volumes (IFAC-PapersOnline)
Number	1
Volume	15
ISSN (Print)	1474-6670

Other

Other	15th World Congress of the International Federation of Automatic Control, 2002
Country/Territory	Spain
City	Barcelona
Period	02/7/21 → 02/7/26

Keywords

High order derivatives
Learning network
Nonlinear system
Stability analysis

ASJC Scopus subject areas

Control and Systems Engineering

Access to Document

10.3182/20020721-6-es-1901.00693

Cite this

Hirasawa, K., Hu, J., & Murata, J. (2002). (N, ε) stability analysis of nonlinear systems using universal learning networks. In G. Ferrate, E. F. Camacho, L. Basanez, & J. A. de la Puente (Eds.), IFAC Proceedings Volumes (IFAC-PapersOnline) (1 ed., pp. 241-246). (IFAC Proceedings Volumes (IFAC-PapersOnline); Vol. 15, No. 1). IFAC Secretariat. https://doi.org/10.3182/20020721-6-es-1901.00693

(N, ε) stability analysis of nonlinear systems using universal learning networks. / Hirasawa, Kotaro; Hu, Jinglu; Murata, Junichi.

IFAC Proceedings Volumes (IFAC-PapersOnline). ed. / Gabriel Ferrate; Eduardo F. Camacho; Luis Basanez; Juan. A. de la Puente. 1. ed. IFAC Secretariat, 2002. p. 241-246 (IFAC Proceedings Volumes (IFAC-PapersOnline); Vol. 15, No. 1).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Hirasawa, K, Hu, J & Murata, J 2002, (N, ε) stability analysis of nonlinear systems using universal learning networks. in G Ferrate, EF Camacho, L Basanez & JA de la Puente (eds), IFAC Proceedings Volumes (IFAC-PapersOnline). 1 edn, IFAC Proceedings Volumes (IFAC-PapersOnline), no. 1, vol. 15, IFAC Secretariat, pp. 241-246, 15th World Congress of the International Federation of Automatic Control, 2002, Barcelona, Spain, 02/7/21. https://doi.org/10.3182/20020721-6-es-1901.00693

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(N, ε) stability analysis of nonlinear systems using universal learning networks

Abstract

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Keywords

ASJC Scopus subject areas

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