Stabilization of Active Fault Tolerant Control Systems with Imperfect Fault Detection and Diagnosis

In active Fault Tolerant Control Systems (FTCSs), a Fault Detection and Diagnosis (FDD) algorithm is used to monitor system performance, detect the occurrence of faults and estimate post-fault system parameters. Usually, estimation techniques employed by the FDD algorithm will provide system parameters with some inaccuracies. As a result, the system to be controlled will include parameter uncertainties. In this paper, exponential stabilization of FTCSs for systems with time-varying unknown-but-bounded parameter uncertainties is considered. In particular, an algorithm that provides a necessary and sufficient condition for exponential stabilization in the mean square is derived. The stabilizing controller is calculated, based on the solutions of matrix Riccatilike algebraic equations. Several interesting special cases are derived from the general result. A numerical example is presented to demonstrate the theoretical developments.