Forced resonant oscillations of nonlinear autonomous system in equilibrium neighborhood. (English. Russian original) Zbl 1230.93040
Autom. Remote Control 71, No. 11, 2360-2366 (2010); translation from Avtom. Telemekh. 2010, No. 11, 112-118 (2010).
Summary: Consideration is given to existence and stability of oscillations in the case of resonance where in the neighborhood of equilibrium the autonomous nonlinear system is subjected to periodic perturbations. For each of the probable cases where the equilibrium is surrounded or not by a family of periodic oscillations, sufficient conditions solving the problem are established. The amplitudes of the resonant oscillations are estimated in terms of a small parameter.
MSC:
| 93C10 | Nonlinear systems in control theory |
| 93C73 | Perturbations in control/observation systems |
| 93D05 | Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory |
| 93C15 | Control/observation systems governed by ordinary differential equations |
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