H − Index for Stochastic Linear Discrete-Time Systems

Model-based fault detection has attracted increasing attention in recent years because of its importance in reliability, security, and fault tolerance of dynamic systems; see [1– 3]. In general, model-based fault detection is related to residual generation, that is, constructing a residual signal and comparing it with a predefined threshold. If the residual exceeds the threshold, an alarm is ringed. However, the residual can change due to the effects of external disturbance and model uncertainty. So fault detection observers must be insensitive to external disturbance and model uncertainty. Some approaches have been given for the design of fault detection observers, such as H

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