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Thus, the problem of designing an observer-based RFDF can be described as designing the observer gain matrix H and the residual weighting matrix V such that
After designing the RFDF, the remaining important task is to decide, from the generated residual, if an alarm has to be generated.
As mentioned in [24, 25], the design of a RFDF for the nonlinear time-delay system (1) can be formulated as an [H.sub.[infinity]] model-matching problem.
As pointed out in , the selection of a suitable reference residual model is one of the key steps to design an RFDF for nonlinear time-delay systems.
The following theorem provides a sufficient condition to ensure that, for a given [alpha] > 0, the reference RFDF satisfies (16).
In this section, we propose a theorem that gives a sufficient condition to guarantee that the RFDF system is stable and has a prescribed [H.sub.[infinity]] performance, independently of the time-delay.
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