FDI (fault detection and isolation) is a crucial part in AFTCS (active fault tolerant control system), so how to model the FDI process and evaluate its influence upon the system is very important. Considering constant networked-induced time delay between sensor and controller in the transmission, two homogeneous Markov stochastic processes with different state spaces were defined: one represented system components failures and the other represented the decisions of the FDI process upon which the state feedback control law was reconfigured. Further, the stability of the control system with state feedback was discussed. A delay-independent sufficient condition based on Kronecker product approachfor checking the mean square stochastic stability of this class of systems was established. Simulation examples were given to demonstrate the theoretical results. Simulation results gave the relation of time-delay, false alarm rate and missed detection rate to guarantee the system stability.