Global Exponential Robust Stability of Generalized Differential Dynamical System With Deviating Argument and Random Disturbance

In this paper, we analyze robust stability of differential dynamical system with deviating argument in derivative part. By using inequality technique and stochastic analysis idea, we obtain the upper bounds of the interval length of deviating argument and the noise intensity, respectively. First, it is proved theoretically that for a given exponentially stable differential dynamical system (DDS), if the interval length of deviating argument is lower than the upper bound, DDS with deviating argument will still maintain exponentially stable. In addition, it is also proved that for a given exponentially stable DDS, if the interval length of deviating argument and noise intensity are lower than the upper bound, stochastic DDS (SDDS) with deviating argument will remain exponentially stable. Finally, theoretical findings are supported by two examples.