Effects of fault detection and isolation to the stability of fault tolerant control systems

In this paper the effect of detection delays and errors on the stochastic stability of Fault Tolerant Control Systems with Markovian Parameters (FTCSMP) is studied. A mathematical representation for the detection delays of a Fault Detection and Isolation (FDI) process is developed. FDI processes employing memory-less statistical and sequential tests are considered. The dynamic programming principle is used to minimize a stochastic cost function and to obtain an optimal control law. Both the failure process and the FDI process are assumed to be available for the controller. Therefore, the designed controller allows the consideration of errors in fault detection. It is shown that the stability of FTCSMP may be lost in the event of large detection delays or errors in detection. A numerical example is used to demonstrate the theoretical developments