Fault tolerance analysis for a class of stochastic systems

This paper models a class of stochastic systems with faults by the switching diffusion processes (SDP), and analyzes the fault tolerability of such stochastic systems in the sense of input-to-state stability (ISS) of overall SDP. A series of sufficient conditions are established to guarantee the ISS of the stochastic systems in spite of faults in three cases respectively: All individual modes of SDP are ISS; Partial modes are ISS, and finally no mode is ISS. The fault tolerability relies on the tradeoff among the fault occurrence transition rate, the frequency of switching, and the decreasing rate of Lyapunov functions along the solution of the system. The proposed tools are illustrated through an example of a manufacturing system.