EXTENDED STABILITY CRITERIA FOR DIFFERENTIAL EQUATIONS VIA LIAPOUNOV THEORY
Abstract
A JUDICIOUS CHOICE OF AN APPROPRIATE QUADRATIC LIAPOUNOV FUNCTION LENDS ITSELF TO GRAPHICAL INTERPRETATION FROM WHICH ONE GAINS INSIGHT INTO LIAPOUNOV'S 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
Document Details
- Document Type
- Technical Report
- Publication Date
- May 16, 1961
- Accession Number
- AD0260573
Entities
People
- William N. Redisch
Organizations
- New York University Tandon School of Engineering