Vibrational Control of Nonlinear Time Delay Systems

This thesis develops the theory of vibrational control of nonlinear time delay systems. 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 to important applications such as an exothermic reaction in a continuous stirred tank reactor and (2) the differences in the theory presented and the existing known theory for vibrational control of ordinary differential equations.