DocumentCode :
796243
Title :
The stability of an nth-order nonlinear time-varying differential system
Author :
Davison, E.J.
Author_Institution :
University of Toronto, Toronto, Canada
Volume :
13
Issue :
1
fYear :
1968
fDate :
2/1/1968 12:00:00 AM
Firstpage :
99
Lastpage :
102
Abstract :
The stability of a system described by an n th order differential equation y^{(n)} + a_{n-1}y^{(n-1)} + . . . + a_{1}y + a_{0} = 0 where a_{i}=a_{i}(t, y, \\dot{y}, . . . , y^{(n-1)}), i=0, 1, . . . , n - 1 , is considered. It is shown that if the roots of the characteristic equation of the system are always contained in a circle on the complex plane with center (-z, 0), z > 0 , and radius Ω such that frac{z}{\\Omega } > 1 + nC_{[n/2]} where [n/2] = nearest integer \\geq n/2 and nC_{m} = n!/m!(n-m)! , where n and m are integers, then the system is uniformly asymptotically stable in the sense of Liapunov.
Keywords :
Nonlinear systems, time-varying; Stability; Time-varying systems, nonlinear; Adaptive control; Aerospace control; Automatic control; Control systems; Delay effects; Learning systems; Regulators; Stability; Time varying systems;
fLanguage :
English
Journal_Title :
Automatic Control, IEEE Transactions on
Publisher :
ieee
ISSN :
0018-9286
Type :
jour
DOI :
10.1109/TAC.1968.1098781
Filename :
1098781
Link To Document :
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