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This paper investigates the stabilization and control problems for linear continuous-time mean-field systems. Under standard assumptions, the necessary and sufficient conditions to stabilize the mean-field systems in the mean-square sense are explored for the first time. It is shown that, under the assumption of exact detectability (exact observability), the mean-field system is stabilizable if and only if a coupled algebraic Riccati equation admits a unique positive-semidefinite solution (positive-definite solution), which coincides with the classical stabilization results for standard deterministic systems and stochastic systems.
Qi et al. (Fri,) studied this question.