On NSS for a class of random time-delay nonlinear systems

Time-delay systems disturbed by white noises were comprehensively modeled as stochastic functional differential equations in the existing literature. However, in some specific situations, they cannot always precisely describe dynamic characters of time-delay systems subject to nonwhite noise disturbances. In this paper, color noises with finite 2-order moments are introduced to time-delay systems (such systems are referred as random ones). First, we present some general conditions to guarantee the existence and uniqueness of solutions to random time-delay systems. Next, in light of these results and Lyapunov function approach, the noise-state stability is analyzed. One example is given to illustrate the effectiveness of the obtained results.