General Stabilization for Stochastic System With Input Delay and Multiplicative Noise: Continuous-time Case

This paper investigates the general stabilization issues for continuous-time stochastic dynamics whose input delay and multiplicative noise in control variable exist simultaneously. On the one hand, we present a set of necessary and sufficient conditions for stabilizing the considered stochastic dynamics in mean-square sense. Different from many previous works, one significant innovation is that our control policy is designed as the feedback of an extended state that contains the current available state and some past control information. On the other hand, another important innovation is that we for the first time generalize the notions of critical stabilization and essential destabilization to stochastic time-delay model in terms of spectral analysis technique, while the related necessary and sufficient stabilization conditions are derived respectively.