Analysis of the stochastic stability for fault tolerant control systems

The analysis of the stochastic stability of fault tolerant control systems (FTCS) has been considered using Lyapunov function approach. A new dynamical model is developed to overcome the limitations of the existing results. In this model, two independent failure processes with Markovian transition probabilities are considered: one for plant components and the other for control actuators. Moreover, the proposed model takes into consideration failures in control actuators with internal dynamics. It is shown that the exponential stability in the mean square is sufficient for the almost sure asymptotic stability, and a necessary and sufficient condition for the exponential stability in the mean square for linear FTCS is derived. Some previously known results are shown to be special cases of these new results. A numerical example is included to demonstrate the theoretical analysis.