Stability analysis of stochastic McKean–Vlasov equations with discrete observation

This paper explores the stability issue of stochastic McKean–Vlasov equations (SMVEs) through an innovative method: stabilization via stochastic delay feedback control with discrete observation. Unlike conventional techniques, this approach leverages historical states instead of solely relying on the current state, setting it apart from traditional stochastic feedback controls. The study examines how the diffusion term contributes to enhancing system stability despite the presence of random fluctuations and delays, guaranteeing both $p$-th moment exponential stability and almost sure exponential stability under a specific delay threshold ${\delta }^{*}$. The primary contributions of this work include introducing a novel stability analysis framework utilizing stochastic delay feedback control, constructing Lyapunov functions that incorporate both state and distribution, and providing insights into asymptotic and moment exponential stability. Although identifying the optimal delay ${\delta }^{*}$ remains a practical challenge, the theoretical foundation laid in this study offers valuable guidance for real-world applications.