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Accession Number:
AD0260573
Title:
EXTENDED STABILITY CRITERIA FOR DIFFERENTIAL EQUATIONS VIA LIAPOUNOV THEORY
Corporate Author:
POLYTECHNIC INST OF BROOKLYN N Y MICROWAVE RESEARCH INST
Report Date:
1961-05-16
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
Descriptive Note:
Research rept.
Supplementary Note:
Master's thesis; report for Sep. 60-Jun 61.
Pages:
0055
Contract Number:
DA30 069ORD2646
File Size:
0.00MB
