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

Tags

Communities of Interest

  • Air Platforms

DTIC Thesaurus Topics

  • Abstracts
  • Coefficients
  • Differential Equations
  • Equations
  • Geometry
  • Mathematics
  • Three Dimensional
  • Two Dimensional

Fields of Study

  • Mathematics

Readers

  • Control Systems Engineering.
  • Fluid Dynamics.
  • Theoretical Analysis.