  This paper is concerned with uniform stabilization and social optimality for
general mean field linear quadratic control systems, where subsystems are
coupled via individual dynamics and costs, and the state weight is not assumed
with the definiteness condition. For the finite-horizon problem, we first
obtain a set of forward-backward stochastic differential equations (FBSDEs)
from variational analysis, and construct a feedback-type control by decoupling
the FBSDEs. For the infinite-horizon problem, by using solutions to two Riccati
equations, we design a set of decentralized control laws, which is further
proved to be asymptotically social optimal. Some equivalent conditions are
given for uniform stabilization of the systems in different cases,
respectively. Finally, the proposed decentralized controls are compared to the
asymptotic optimal strategies in previous works.
