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Barbanti, L.; Damasceno, B. C.

Control aspects in nonlinear Hill’s equation. (English) Zbl 1221.34166

Commun. Nonlinear Sci. Numer. Simul. 16, No. 5, 2328-2331 (2011).
Summary: The Hill’s equations – even in the linear original version – describe phenomena having chaotic flavor. The theory of the so called intervals of instability in the equation provides the precise description for most of these phenomena. Considerations on nonlinearities into the Hill’s equation is a quite recent task. The linearized version for almost of these systems reduces it to the Hill’s classical linear one. In this paper, some indicative facts are pointed out on the possibility of having the linear system stabilizable and/or exactly controllable. As consequence of such an approach we get results having strong classical aspects, like the one talking about location of parameters in intervals of stability. A result for nonlinear proper periodic controls, is considered too.

Cited in 1 Document

MSC:

34H15 Stabilization of solutions to ordinary differential equations
34B30 Special ordinary differential equations (Mathieu, Hill, Bessel, etc.)
34H05 Control problems involving ordinary differential equations
93B05 Controllability

Keywords:

nonlinear Hill’s equation; controlled Hill’s equation; periodic solutions; stability
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\textit{L. Barbanti} and \textit{B. C. Damasceno}, Commun. Nonlinear Sci. Numer. Simul. 16, No. 5, 2328--2331 (2011; Zbl 1221.34166)
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