Due to increased efforts on digitizing the modern power electronic systems and microgrids, their operational reliability and stability are prone to the risk of cyber attacks. In this paper, we inspect the overlooked stability issues caused by cyber-attacks, and present an overall design insight for stabilization of microgrids under cyber attacks. Firstly, we shed light on the optimal design policy and sensitivity aspects of the solution for microgrids under cyber-attacks. These results are based on a describing function-based modeling method to map the stability region. Secondly, the sensitivity impact due to system parameter variations and stabilization gains on stability is theoretically investigated. In addition, the range of sensitivity of parameter variations with respect to cyber attacks are calculated. Based on different design requirements, optimal values are theoretically obtained and then tested on microgrids having different parameters in a simulation environment, which justifies the ruggedness of the proposed design approach. We provide a generalized philosophy, which can be easily extended to the overall design, stability and parameter sensitivity of cyber-physical energy systems.