A counterpart of Popov's theorem for the existence of periodic solutions†

1 April 1971

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

Vol. 13 (4) , 705-719
https://doi.org/10.1080/00207177108931977

Abstract

Sufficient conditions are given for the existence of non-trivial periodic solutions for the equation of a class of time-invariant, non-linear feedback systems. The criteria rely on familiar principles in topology and are presented in such a form that they constitute an oscillation counterpart of Popov's stability theorem.

Keywords

This publication has 2 references indexed in Scilit:

A Frequency Domain Approach to the Problem of the Existence of Periodic Motion in Autonomous Nonlinear Feedback Systems
ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, 1969
Frequency-domain instability criteria for time-varying and nonlinear systems
Proceedings of the IEEE, 1967