A complete methodology to design robust Fault Detection and Isolation (FDI) filters and Fault Tolerant Control (FTC) schemes for Linear Time-Varying (LTV) systems is proposed. The paper takes advantage of the recent advances in model invalidation using Set-Valued Observers (SVOs) that led to the development of FDI methods for uncertain linear time-varying systems, with promising results in terms of the time required to diagnose faults. An integration of such SVO-based FDI methods with robust control synthesis is described, in order to deploy new FTC algorithms that are able to stabilize the plant under faulty environments. The FDI algorithm is assessed within a wind turbine benchmark model, using Monte-Carlo simulation runs.