Abstract
AbstractThis paper presents a necessary and sufficient condition for the fault detection (FD) problem, under a quite general and natural assumption. The condition is actually a constant inertia on the extended imaginary axis (EIA) of a para‐hermitian rational matrix (RM). An observer solution is given. Another two main results are the presentation of all problem solutions, and a necessary and sufficient condition for constant inertia on the EIA or in a given frequency region, for a class of para‐hermitian RMs, in terms of linear matrix inequalities. The latter result can be regarded as a generalization of the Kalman‐Yakubovich‐Popov (KYP) lemma.
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