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

Kotaro Hirasawa, Takayuki Furuzuki, Junichi Murata

Research output: Chapter in Book/Report/Conference proceedingConference 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 languageEnglish
Title of host publicationIFAC Proceedings Volumes (IFAC-PapersOnline)
PublisherIFAC Secretariat
Pages241-246
Number of pages6
Volume15
Edition1
Publication statusPublished - 2002
Externally publishedYes
Event15th World Congress of the International Federation of Automatic Control, 2002 - Barcelona, Spain
Duration: 2002 Jul 212002 Jul 26

Other

Other15th World Congress of the International Federation of Automatic Control, 2002
CountrySpain
CityBarcelona
Period02/7/2102/7/26

Fingerprint

Nonlinear systems
Derivatives
Trajectories

Keywords

  • High order derivatives
  • Learning network
  • Nonlinear system
  • Stability analysis

ASJC Scopus subject areas

  • Control and Systems Engineering

Cite this

Hirasawa, K., Furuzuki, T., & Murata, J. (2002). (N, ε) stability analysis of nonlinear systems using universal learning networks. In IFAC Proceedings Volumes (IFAC-PapersOnline) (1 ed., Vol. 15, pp. 241-246). IFAC Secretariat.

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

IFAC Proceedings Volumes (IFAC-PapersOnline). Vol. 15 1. ed. IFAC Secretariat, 2002. p. 241-246.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Hirasawa, K, Furuzuki, T & Murata, J 2002, (N, ε) stability analysis of nonlinear systems using universal learning networks. in IFAC Proceedings Volumes (IFAC-PapersOnline). 1 edn, vol. 15, IFAC Secretariat, pp. 241-246, 15th World Congress of the International Federation of Automatic Control, 2002, Barcelona, Spain, 02/7/21.
Hirasawa K, Furuzuki T, Murata J. (N, ε) stability analysis of nonlinear systems using universal learning networks. In IFAC Proceedings Volumes (IFAC-PapersOnline). 1 ed. Vol. 15. IFAC Secretariat. 2002. p. 241-246
Hirasawa, Kotaro ; Furuzuki, Takayuki ; Murata, Junichi. / (N, ε) stability analysis of nonlinear systems using universal learning networks. IFAC Proceedings Volumes (IFAC-PapersOnline). Vol. 15 1. ed. IFAC Secretariat, 2002. pp. 241-246
@inproceedings{40879c08373140829246efdbc795bae1,
title = "(N, ε) stability analysis of nonlinear systems using universal learning networks",
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.",
keywords = "High order derivatives, Learning network, Nonlinear system, Stability analysis",
author = "Kotaro Hirasawa and Takayuki Furuzuki and Junichi Murata",
year = "2002",
language = "English",
volume = "15",
pages = "241--246",
booktitle = "IFAC Proceedings Volumes (IFAC-PapersOnline)",
publisher = "IFAC Secretariat",
edition = "1",

}

TY - GEN

T1 - (N, ε) stability analysis of nonlinear systems using universal learning networks

AU - Hirasawa, Kotaro

AU - Furuzuki, Takayuki

AU - Murata, Junichi

PY - 2002

Y1 - 2002

N2 - 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.

AB - 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.

KW - High order derivatives

KW - Learning network

KW - Nonlinear system

KW - Stability analysis

UR - http://www.scopus.com/inward/record.url?scp=84945567446&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84945567446&partnerID=8YFLogxK

M3 - Conference contribution

VL - 15

SP - 241

EP - 246

BT - IFAC Proceedings Volumes (IFAC-PapersOnline)

PB - IFAC Secretariat

ER -