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

1 March 1965

journal article
research article
Published by Taylor & Francis in International Journal of Control

Vol. 1 (3) , 209-216
https://doi.org/10.1080/00207176508905473

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.

Keywords

This publication has 2 references indexed in Scilit:

THEORY OF THE ANALYSIS OF NONLINEAR SYSTEMS
Published by Defense Technical Information Center (DTIC) ,1958
Inequalities for solutions of linear differential equations a contribution to the theory of servomechanisms
Edinburgh Mathematical Notes, 1952