Automatic Control and Systems Engineering, University of Sheffield
Abstract
The Volterra series representation is a direct generalisation of the linear convolution integral and has been widely applied in the analysis and design of
nonlinear systems, both in the time and the frequency domain. The Volterra series is associated with the so-called weakly nonlinear systems, but even within the
framework of weak nonlinearity there is a convergence limit for the existence of a valid Volterra series representation for a given nonlinear differential equation.
Barrett(1965) proposed a time domain criterion to prove that the Volterra series converges with a given region for a class of nonlinear systems with cubic stiffness
nonlinearity. In this paper this time-domain criterion is extended to the frequency domain to accommodate the analysis of nonlinear oscillators subject to harmonic
excitation
