Stability of periodic solutions of a non-linear differential equation arising in servomechanism theory
Titel:
Stability of periodic solutions of a non-linear differential equation arising in servomechanism theory
Auteur:
Christopher, P. A. T.
Verschenen in:
International journal of control
Paginering:
Jaargang 26 (1977) nr. 6 pagina's 901-915
Jaar:
1977-12-01
Inhoud:
The stability of the periodic solutions of a particular non-linear differential equation of third order is discussed in terms of the asymptotic stability of the corresponding variational equation and, thereby, in terms of the characteristic exponents of this equation. A method, due to Cesari, is used to evaluate the characteristic exponents and thus the boundaries of asymptotic stability. Taking the solution to have, in the first approximation, an amplitude F and frequency ω, it is shown that one of the asymptotic stability boundaries corresponds to the locus of vertical tangents of the frequency response curves in the ω, F plane. This result is similar in character to, and a modest generalization of, the well-known stability criterion associated with Duffing's equation.
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