New Condition for FD, All Filters, and New KYP Lemma

Abstract

This paper presents a necessary and sufficient condition for the ℋ − ∕ℋ ∞ 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. Key Words:Fault detection in presence of disturbances, J-spectral factorization, inertia of hermitian matrix, finite and infinite zeros.