An input-state-output inclusion principle for linear stochastic systems is proposed, with the emphasis on restriction and aggregation conditions for estimators and dynamic controllers. Inclusion of the LQG (linear quadratic Gaussian) optimal design is formulated and applied to the decentralized overlapping control of large-scale interconnected systems. Applications of the proposed methodology are illustrated using a stochastic model of automatic generation control (AGC) for interconnected power systems. Three types of overlapping decentralized and fully decentralized dynamic controllers, consisting of state estimators and feedback gains, are proposed for the cases of full and reduced measurement sets. An extensive analysis of both steady-state and transient regimes under a variety of operating conditions shows the superiority of the proposed AGC scheme with respect to the standard AGC designs.