Stochastic stability analysis for fault tolerant control systems with multiple failure processes

A new dynamical model is developed here to study the stochastic stability of Fault Tolerant Control Systems (FTCS) with multiple failure processes. In particular, two independent failure processes with Markovian characteristics are considered: one for plant component failures and the other for actuator failures. In this model, the Fault Detection and Isolation (FDI) process is also formulated as a Markov process with transition probabilities conditioned on the current state transition probabilities of the two failure processes. It is shown that the exponential stability in the mean square is su cient for almost sure asymptotic stability. In addition, a necessary and su cient condition for exponential stability in the mean square for FTCS is derived. Some previously known results are shown to be special cases of this new result. Failures in actuators with internal dynamics are also considered. A numerical example is included to demonstrate the theoretical analysis.