An improved frequency time domain stability criterion for autonomous continuous systems

Author

O´Shea, R.

Author_Institution

US Steel Applied Research Laboratories, Monroeville, PA, USA

Volume

Issue

fYear

1967

fDate

12/1/1967 12:00:00 AM

Firstpage

725

Lastpage

731

Abstract

A sufficient condtion given for the asymptotic stability of a system having a single monotonic nonlinearity with slope confined to $[0, k_{2}]$ and a transfer function $G(j\\omega )$ , is $\\Re (1 + X(j\\omega ) + Y(j\\omega ) + \\alpha j\\omega )(G(j\\omega ) + 1/k_{2}) \\geq 0$ where $\\alpha > 0 , x(t)\\leq 0$ for $t \\leq 0$ and $x(t)=0$ for $t> 0 , y(t)\\leq0$ for $t> 0$ and $y(t) = 0$ for $t < 0$ , and $\\int\\min{-\\infty }\\max {\\infty }(| x(t)| + | y(t) | )dt < 1$ . The improvement consists of the addition of the $X(j\\omega )$ term which corresponds to a nonzero time function for $t< 0$ , resulting in $Z(j\\omega )$ multipliers whose phase angle is capable of varying from +90° to -90° any desired number of times. As is shown by examples, the new criterion gives better results than existing criteria. Also developed is an improved criterion for an odd monotonic nonlinearity.

Keywords

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

fLanguage

English

Journal_Title

Automatic Control, IEEE Transactions on

Publisher

ieee

ISSN

0018-9286

Type

jour

DOI

10.1109/TAC.1967.1098725

Filename

1098725

Link To Document

https://search.isc.ac/dl/search/defaultta.aspx?DTC=49&DC=795638