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.