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In this paper active fault-tolerant control (FTC) is designed in a stochastic framework. The fault-tolerant control system (FTCS) is formulated as a set of linear systems governed by two continuous-time finite-state Markov chains, which are used to characterise the system failure modes and the fault detection and isolation (FDI) scheme. This framework is widely accepted for stability analysis of FTCS; however, the design of a controller only accessing the FDI mode is still a challenging problem. We solve this synthesis problem by using convex optimisation techniques. First, a sufficient condition for the mean exponential stability is given in terms of a linear matrix inequality (LMI). The results are then extended to uncertain systems design for stability and in system performance using a stochastic integral quadratic constraint. Due to the complexity of the problem, the controller is obtained using the iterative LMI technique.