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

In this paper, we study the stability of solutions stochastic McKean--Vlasov equations via feedback control based on discrete-time state observation. By using a specific Lyapunov function, $H_{\infty}$ stability, asymptotic and exponential in mean square for solution controlled systems are obtained. Since distribution is difficult to observe, corresponding particle system which can be observed control. We prove that equivalent system. Finally, an example provided show effectiveness theory.