Accession Number:

AD0260573

Title:

EXTENDED STABILITY CRITERIA FOR DIFFERENTIAL EQUATIONS VIA LIAPOUNOV THEORY

Descriptive Note:

Research rept.

Corporate Author:

POLYTECHNIC INST OF BROOKLYN N Y MICROWAVE RESEARCH INST

Personal Author(s):

Report Date:

1961-05-16

Pagination or Media Count:

55.0

Abstract:

A JUDICIOUS CHOICE OF AN APPROPRIATE QUADRATIC LIAPOUNOV FUNCTION LENDS ITSELF TO GRAPHICAL INTERPRETATION FROM WHICH ONE GAINS INSIGHT INTO LIAPOUNOVS THEORY, RATHER THAN GETTING TANGLED IN THE MATHEMATICAL ABSTRACTS. THIS GRAPHICAL APPROACH LEADS TO MUCH VALUABLE INFORMATION ABOUT THE BEHAVIOR OF THE SOLUTION TO A LINEAR HOMOGENEOUS DIFFERENTIAL EQUATION WITH TIME-VARYING COEFFICIENTS. WITHOUT HAVING TO SOLVE THE DIFFERENTIAL EQUATION, IT IS POSSIBLE TO DRAW CONCLUSIONS ABOUT THE STABILITY OF THE SOLUTION. PRINCIPLES ARE READILY ESTABLISHED FOR A FIRSTORDER EQUATION VIA A TWO-DIMENSIONAL PLANE, AND MAY GENERALLY BE EXTENDED TO SECOND-ORDER EQUA-TIONS VIA A THREE-DIMENSIONAL S7AC5

Subject Categories:

Distribution Statement:

APPROVED FOR PUBLIC RELEASE