Aiming at restructuring the conventional energy delivery infrastructure, the concept of energy Internet (EI) has become popular in recent years. Outstanding benefits from an EI include openness, robustness and reliability. Most of the existing literatures focus on the conceptual design of EI and are lack of theoretical investigation on developing specific control strategies for the operation of EI. In this paper, a class of control strategies for EI considering system robustness and operation cost optimization is investigated. Focusing on the EI system robustness issue, system parameter uncertainty, external disturbance and tracking error are taken into consideration, and we formulate such robust control issue as a structure specified mixed H 2 /H ∞ control problem. When formulating the operation cost optimization problem, three aspects are considered: realizing the bottom-up energy management principle, reducing the cost involved by power delivery from power grid (PG) to microgrid (MG), and avoiding the situation of over-control. We highlight that this is the very first time that the above targets are considered simultaneously in the field of EI. The integrated control issue is considered in frequency domain and is solved by a particle swarm optimization (PSO) algorithm. Simulation results show that our proposed method achieves the targets.