Wind energy is the fastest growing and the most promising renewable energy resource. High efficiency and reliability are required for wind energy conversion systems (WECSs) to be competitive within the energy market. Difficulties in achieving the maximum level of efficiency in power extraction from the available wind energy resources warrant the collective attention of control and power system engineers. A strong movement toward sustainable energy resources and advances in control system methodologies make previously unattainable levels of efficiency possible. In this paper, we design a general resilient and robust control framework for a time-delay variable speed permanent magnet synchronous generator (PMSG)-based WECS. A linear matrix inequality-based control approach is developed to accommodate the unstructured model uncertainties, type of external disturbances, and time delays in input and state feedback variables. Computer simulation results have shown the efficacy of the proposed approach of achieving asymptotic stability and performance objectives.