A combined frequency-time domain stability criterion for autonomous continuous systems

Author

O´shea, R.P.

Author_Institution

University of Pittsburgh, Pittsburgh, PA, USA

Volume

Issue

fYear

1966

fDate

7/1/1966 12:00:00 AM

Firstpage

477

Lastpage

484

Abstract

An improved sufficient condition for asymptotic stability developed for the monotone nonlinearity is $\\Re [Z(j\\omega ) (G(j\\omega ) + 1/k_{2})]$ or $\\Re [Z(j\\omega ,) \\bar(G(j\\omega ) + 1/k_{2})] \\geq 0$ where $Z(s)=1+\\alpha s+Y(s)$ and $\\int\\min{0}\\max {\\infty }|y(t)|dt< 1$ . Examples of allowed $Z(s)$ functions are considered which show that the angle of $G(j\\omega ) +1/k_{2}$ is permitted to take on both positive and negative values outside the $\\pm90\\deg$ band. The approach used in deriving the above results is a general one which reduces the problem of obtaining sufficient conditions for asymptotic stability to one of obtaining a bound for a cross-correlation function $R(T)$ in terms of $R(O)$ . As an example, a sufficient condition for asymptotic stability is developed for a continuous nonlinearity having a monotone bound which appears to have considerable practical application.

Keywords

Asymptotic stability; Nonlinear systems, continuous-time; Asymptotic stability; Continuous time systems; Stability criteria; Sufficient conditions; Transfer functions;

fLanguage

English

Journal_Title

Automatic Control, IEEE Transactions on

Publisher

ieee

ISSN

0018-9286

Type

jour

DOI

10.1109/TAC.1966.1098402

Filename

1098402

Link To Document

https://search.isc.ac/dl/search/defaultta.aspx?DTC=49&DC=792302