Optimal filtering, fault detection and isolation for linear discrete time systems in a noisy environment

In this paper the state observer design and the fault detection and isolation problems are investigated in the context of linear discrete-time state-space models whose state equations are affected by (actuator) faults and disturbances. Model as well as measurement errors, described as zero-mean white Gaussian noise, are also assumed to act additively on the state and on the output equations, respectively. Upon introducing several deterministic and stochastic goals, that constitute the mathematical formalization of very natural and practical requirements, necessary and sufficient conditions for the existence of an asymptotic state observer and an observer-based fault detector and isolator, that achieve the above goals, are finally derived and a constructive procedure is described.