The stability of an nth-order nonlinear time-varying differential system

Author

Davison, E.J.

Author_Institution

University of Toronto, Toronto, Canada

Volume

Issue

fYear

1968

fDate

2/1/1968 12:00:00 AM

Firstpage

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

https://search.isc.ac/dl/search/defaultta.aspx?DTC=49&DC=796243