Improving stability of time-delayed systems with rapidly and periodically time-varying perturbation to the delay

Time-varying delay usually deteriorates the stability of systems and leads to complex dynamics. In present paper, it is shown, under certain conditions, the stability can be improved by introducing a rapidly and periodically time-varying perturbation to the constant delay. On the basis of center manifold theorem and averaging method, the practical stability conditions are obtained, under which the stability of the time-delayed system is improved by introducing a rapidly and periodically perturbation to the constant delay. Case study indicates that the analytical results agree with numerical results very well.