AN INVESTIGATION OF ONE NONLINEAR SYSTEM OF THREE DIFFERENTIAL EQUATIONS

Abstract

Statements (without proof) are given for two lemmas an twelve theorems yielding constraints on system parameters and nonlinearity for asymptotic sta ility in the large and boundedness of solutions of a system of the following three Aizerman-type equations: dx = y - f(x), dy = z - x, and dz = ax - bf(x). A method is also advanced for constructing a Lyapunov function for Aizerman-type s stems; these Lyap nov functions are of the form: integral of the nonlinearity plus a quadratic form in the state variables. Two of t e twelve theorems yield sufficient conditions for the existence of periodic solutions of the above system; much of the discussion evolves about when satisfaction of the generalized Routh- hurwitz implies stability in the large for the n ll solution. No examples or indication towards practical application of the theorems i given. (Author)

Document Details

Document Type
Technical Report
Publication Date
May 01, 1961
Accession Number
AD0264058

Entities

People

  • V.a. Pliss

Organizations

  • TRW Inc.

Tags

DTIC Thesaurus Topics

  • Differential Equations
  • Equations
  • Integrals
  • Linear Differential Equations
  • Lyapunov Functions
  • Mathematical Analysis
  • Mathematics
  • Nonlinear Differential Equations
  • Nonlinear Systems

Fields of Study

  • Mathematics

Readers

  • Control Systems Engineering.
  • Mathematical Modeling and Probability Theory.
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