Gain-Scheduled Fault Detection Filter for Discrete-Time LPV Systems

The present work investigates a fault detection problem using a gain-scheduled filter for discrete-time Linear Parameter Varying systems. We assume that we cannot directly measure the scheduling parameter but, instead, it is estimated. On the one hand, this assumption imposes the challenge that the fault detection filter should perform properly even when using an inexact parameter. On the other, it avoids the burden associated with designing a complex estimation process for this parameter. We propose three design approaches: the
${\mathcal {H}_{2}}$
,
${\mathcal {H}_{\infty }}$
, and mixed
${\mathcal {H}_{2}} / {\mathcal {H}_{\infty }}$
gain-scheduled Fault Detection Filters designed via Linear Matrix Inequalities. We also provide numerical simulations to illustrate the applicability and performance of the proposed novel methods.