Vibrational control of a class of nonlinear systems by nonlinear multiplicative vibrations

Vibrational control is a nonclassical control principle which proposes a utilization of zero mean parametric excitation of a dynamical system for control purposes. This paper extends nonlinear vibrational control theory developed in [8,9] to systems controlled by nonlinear multiplicative vibrations. Condition for vibrational stabilizability with respect to a component of a steady-state vector, the choice of stabilizing vibrations and the transient motions are discussed for a certain practically important class of nonlinear vibrationally controlled systems. The application of the results is demonstrated on the example of a catalytic reactor, using a combination of numerical and analytical techniques.