Stability analysis of stochastic McKean–Vlasov equations with discrete observation

• This paper investigates the stabilizing effect of the diffusion term on the p th moment exponential stability of SMVDEs. We examine how the diffusion term contributes to system stability, ensuring robustness against random fluctuations and delays. • We introduce a novel approach based on stochastic delay feedback control, where system (1.2) is compared with system (1.1) to guarantee p th moment exponential stability. Additionally, we establish its almost sure exponential stability and provide an implicit lower bound for ??. • The Lyapunov functions used in this study consider both the state and the distribution of the solution, whereas traditional Lyapunov functions in state feedback control systems focus solely on the state. This distinction is a notable feature of our approach. • We explore the asymptotic stability and mean square exponential stability of SMVEs under discrete-time state observations. 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 δ * . 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 δ * remains a practical challenge, the theoretical foundation laid in this study offers valuable guidance for real-world applications.