Vibrational control of nonlinear time lag systems: Vibrational stabilization and transient behavior

This paper addresses two problems of control of nonlinear time lag systems: (i) an existence and a synthesis of parametric vibrations for their stabilization and (ii) the transient behavior analysis of the vibrationally controlled nonlinear systems with time lags. In this work, stabilizability conditions for two vibration types are formulated and procedures for the synthesis of the corresponding stabilizing vibrations are proposed. The method for the transient behavior analysis of vibrationally controlled systems on a finite time interval is developed as well. Several examples are given to support the theory presented.