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 |
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Keywords
- High order derivatives
- Learning network
- Nonlinear system
- Stability analysis
ASJC Scopus subject areas
- Control and Systems Engineering
Cite this
(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 proceeding › Conference contribution
}
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 -