Stochastic stability analysis of fault-tolerant control systems in the presence of noise

The stochastic stability of fault tolerant control systems (FTCSs) in the presence of noise are,analyzed using the Lyapunov function approach. In particular, the FTCS with a Markovian fault detection and isolation process having transition probabilities conditioned on the state of another Markovian process representing component failures, is considered. The almost sure asymptotic stability in probability and the exponential stability in the mean square are considered. Specifically, a testable necessary and sufficient condition for the exponential stability in the mean square is derived. A numerical example is presented to illustrate the theoretical analysis.