Characterization of Stochastic Mean-Field Type H− Index

H− index of mean-field stochastic differential equations (SDE) is investigated in this paper. For systems with state- and input-dependent noise, we obtain a sufficient condition of H− index larger than some λ>0 via the solvability of differential Riccati equations (DRE). Especially, a necessary and sufficient condition is given for mean-field SDE with state-dependent noise, which generalize the corresponding results of classical stochastic systems to the mean-field stochastic models.