ON THE EXISTENCE OF LYAPUNOV FUNCTIONS IN THE CASE OF ASYMPTOTIC STABILITY IN THE LARGE

Abstract : Definitions on stability are given among which is included a detailed definition of stability in the large of two systems with time delay. Two theorems are stated with detailed proofs for solution of these systems. From the proof of theorem two, the question of the stability of a system of equations with respect to time delays is similar to the problem of the stability of motion for continuously operative disturbances.