Resonant Oscillations of the Coupled Controlled System Near Equilibrium

We consider a nonlinear autonomous coupled system of a general type in the vicinity of equilibrium. It is assumed that the linear approximation matrix has a pair of purely imaginary eigenvalues; other eigenvalues are not multiples of the specified ones and are different from zero. We study the oscillations under the action of a periodic controls with a small regulator gain. The existence of a resonant oscillation of the controlled system is established, the oscillation amplitudes are estimated in terms of the value of regulator gain, the stability of the oscillation is analyzed. Previously, the result was known for the Lyapunov system.