Noise expresses exponential decay for globally exponentially stable nonlinear time delay systems

In this paper, we show that noise can make a given nonlinear time delay system which is globally exponentially stable become a new stochastic one whose solution to exponential decay faster than the former. By comparing the upper bounds of noise intensity and coefficients of global exponential stability, we could deduce that noise is able to further express exponential decay for nonlinear time delay system without losing global stability. The upper bounds of noise intensity are characterized by solving transcendental equations containing adjustable parameters. In addition, a numerical example is provided to illustrate the theoretical result.