Vibrational control of nonlinear systems: Vibrational stabilizability

In this work, the theory of vibrational control for nonlinear systems is developed. The present paper gives criteria for stabilizability of nonlinear systems by linear multiplicative vibrations, by almost periodic forcing and by vector additive vibrations. Illustrative examples are also considered. In a subsequent paper, the problem of vibrational controllability and transient behavior will be addressed.