Stabilization of Stochastic McKean-Vlasov Equations with Feedback Control Based on Discrete-Time State Observation

In this talk, the stability  of solutions of stochastic McKean-Vlasov equations (SMVEs) via feedback control based on discrete-time state observation is investigated, which includes  the $H_{\infty}$ stability, asymptotic stability and  exponential stability in mean square. Since the distribution of  solution is  difficult to be observed, we study  the corresponding particle system which can be  observed for the feedback control.  We  show that the exponential stability of control system  is equivalent to   the  the exponential stability of  the corresponding particle system. Moreover, we will give   an example  to illustrate the theory.