Stochastic Stability Analysis for Continuous Time Fault Tolerant Control Systems

Active fault tolerant control systems are feedback control systems that reconfigure the control law in real time based on the response from an automatic failure detection and identification (FDI) scheme. The dynamic behavior of such systems is characterized by stochastic differential equations because of the random nature of the failure events and the FDI decisions. The stability analysis of these systems is addressed in this paper using stochastic Lyapunov functions and supermartingale theorems. Both exponential stability in the mean square and almost sure asymptotic stability in probability are addressed. In particular, for linear systems where the coefficients of the closed loop system dynamics are functions of two random processes with Markovian transition characteristics (one representing the random failures and the other representing the FDI decision behavior), necessary and sufficient conditions for exponential stability In the mean square are developed.