| The synthesis of a fault tolerant control law for linear systems that takes into account the random decision errors and delays associated with the failure detection scheme is presented. Under these conditions, when the control gains are reconfigured in response to the failure indications, the stability analysis of the resulting closed loop system that is governed by stochastic differential equations is addressed. This analysis makes use of stochastic Lyapunov functions and supermartingale theorems. Both exponential stability in the mean square and almost sure asymptotic stability in probability of all sample solutions of the given system are addressed. In particular, for linear systems, when the coefficients of the closed loop system dynamics are functions of two random processes with Markovian transition characteristics, necessary and sufficient conditions for exponential stability in the mean square of the solution are developed. Extension of these results to cases where one of the random processes has semi-Markovian transition characteristics is also investigated. |
