Accession Number : AD0466778

Title :   STABILITY OF A CLASS OF DIFFERENTIAL EQUATIONS WITH A SINGLE NONLINEARITY.

Descriptive Note : Interim technical rept.,

Corporate Author : HARVARD UNIV CAMBRIDGE MA CRUFT LAB

Personal Author(s) : Narendra, Kumpati S. ; Neuman, Charles P.

Report Date : 28 APR 1965

Pagination or Media Count : 25

Abstract : The absolute stability of a class of dynamical systems with a single nonlinearity which satisfy neither the Popov not the extended Popov theorem is investigated in great detail. Specifically, by reexamining the new Lyapunov function introduced recently by the authors and utilizing the Kalman lemma, frequency domain stability criteria are obtained for the linear plant G(s) in the case of both monotone increasing and odd monotone increasing nonlinearities. For infinite sector problems these criteria are applicable to linear plants whose numerator dynamics have some real non-zero zeros; for finite sector problems these criteria are applicable to systems whose characteristic equation evaluated at the maximum stable feedback gain has some real non-zero zeros or real non-zero poles. The results presented here demonstrate that the stability criteria on the linear plant are even weaker in the case of odd monotone increasing nonlinearities than in the case of monotone increasing nonlinearities. (Author)

Descriptors :   (*DIFFERENTIAL EQUATIONS, FUNCTIONS(MATHEMATICS)), STABILITY, NONLINEAR SYSTEMS, FEEDBACK, THEOREMS, TOPOLOGY.

Distribution Statement : APPROVED FOR PUBLIC RELEASE