The Use of Volterra Series to Find Region of Stability of a Non-linear Differential Equation†

Abstract

This report discusses a special problem which illustrates a new approach for discussing stability of non-linear systems under arbitrary input disturbances. The system is assumed to be described by a non-linear differential equation with forcing term. This equation is solved by 8 type of power series (Volterra series) which gives output explicitly in terms of input. Proof of convergence of this series gives criteria for stability of the system.