Accession Number : AD0264058

Title :   AN INVESTIGATION OF ONE NONLINEAR SYSTEM OF THREE DIFFERENTIAL EQUATIONS

Corporate Author : TRW SPACE TECHNOLOGY LABS LOS ANGELES CALIF

Personal Author(s) : PLISS,V.A.

Report Date : MAY 1961

Pagination or Media Count : 1

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)

Descriptors :   *DIFFERENTIAL EQUATIONS, *NONLINEAR DIFFERENTIAL EQUATIONS, FUNCTIONS(MATHEMATICS), INTEGRALS, NONLINEAR SYSTEMS, TRANSLATIONS

Distribution Statement : APPROVED FOR PUBLIC RELEASE