Abstract
This paper investigates the problem of fault detection for linear discrete time-varying systems with delayed state by using Hi/H∞ and/or Hi/H∞ optimization. A residual generator, which is the so-called Hi/H∞ fault detection filter (FDF), is designed by finding filter gain matrices and a post-filter. By utilizing projection and innovation re-organization technique, an optimal Hi/H∞ -FDF can be given in terms of recursions. Moreover, the obtained evaluation function is a unified solution and, in order to detect the presence of a fault, the selection of a threshold is dependent on the characteristics of unknown input and a prescribed false alarm rate. A numerical example is used to demonstrate the effectiveness of the proposed method.
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