Vibrational control of nonlinear time lag systems with arbitrarily large but bounded delay: averaging theory, stabilizability, and transient behavior

The authors develop the theory of vibrational control of nonlinear time lag systems with arbitrarily large but bounded delay. The averaging theory for fast oscillating differential delay equations is presented and then applied to vibrational control. Conditions are given which ensure the existence of parametric vibrations that stabilize nonlinear time lag systems. Transient behavior is also discussed. Illustrative examples are given which show (1) the feasibility of the theory for important applications and (2) the differences in the theory presented and the known theory for vibrational control of ordinary differential equations