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

Kotaro Hirasawa; Takayuki Furuzuki; Junichi Murata

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

Kotaro Hirasawa, Takayuki Furuzuki, 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)
Publisher	IFAC Secretariat
Pages	241-246
Number of pages	6
Volume	15
Edition	1
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

Other

Other	15th World Congress of the International Federation of Automatic Control, 2002
Country	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

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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",

note = "15th World Congress of the International Federation of Automatic Control, 2002 ; Conference date: 21-07-2002 Through 26-07-2002",

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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

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M3 - Conference contribution

AN - SCOPUS:84945567446

VL - 15

SP - 241

EP - 246

BT - IFAC Proceedings Volumes (IFAC-PapersOnline)

PB - IFAC Secretariat

T2 - 15th World Congress of the International Federation of Automatic Control, 2002

Y2 - 21 July 2002 through 26 July 2002

ER -