Identification of input-output (IO) dynamics of brain networks in response to electrical stimulation is essential for devising closed-loop therapies for neurological disorders such as major depression. A critical component for accurate IO identification is the stimulation input design. The time available for open-loop stimulation to perform system identification is typically limited. While our prior design of a binary noise (BN) modulated input pattern satisfies the requirements for optimal identification and clinical safety, it does not incorporate any prior information about the underlying network. When the identification time is constrained, BN identification performance may be improved by incorporating such information. Here we design a generalized binary noise (GBN) modulated stimulation pattern that achieves time-efficient identification of IO dynamics by utilizing the time-constant information of the network. To test GBN's performance, we implemented a closed-loop controller within a clinical stimulation system. We used our closed-loop system to control mood symptoms in depression using simulated neural activity under linear network dynamics. With a short identification time (20 mins), the controller derived from GBN identification performed as well as an ideal controller that had full knowledge of the network model, and better than a controller derived from BN identification. Our results have important implications for optimal system identification and closed-loop control of brain network dynamics.