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Noise-to-state stability analysis for a class of random time-delay nonlinear systems

Time-delay systems disturbed by white noise have been comprehensively modelled as stochastic functional differential equations in the existing literature. However, in some specific situations, they cannot always precisely describe the dynamic character of time-delay systems subject to non-white noise disturbances. In this paper, colour noises with finite two-order moments are introduced to time-delay systems (such systems are referred to 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 the Lyapunov function approach, the noise-to-state stability and eλt-weighted integral noise-to-state stability are analysed, respectively. One example is given to illustrate the effectiveness of the obtained results.