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Stability conditions for discrete time fault tolerant control systems in noisy environments

A new discrete time fault tolerant control system (DTFTCS) model is developed. The model represents a discrete version of fault tolerant control systems with Markovian parameters (FTCSMP). The proposed model is consistent with the general class of FTCSMP by defining two Markovian processes: one for fault detection and isolation (FDI) and the second represents the failures in control actuators. Stability definitions for DTFTCS are stated and necessary and sufficient conditions for the second moment stability are derived. Second moment stability conditions for a given controller are constructed in terms of feasibility solutions of linear matrix inequalities (LMI).