On Design of Robust Fault Detection Filter in Finite-Frequency Domain With Regional Pole Assignment

This brief is concerned with the fault detection (FD) filter design problem for an uncertain linear discrete-time system in the finite-frequency domain with regional pole assignment. An optimized FD filter is designed such that: 1) the FD dynamics is quadratically
$D$
-stable; 2) the effect from the exogenous disturbance on the residual is attenuated with respect to a minimized
$H_{\infty} $
-norm; and 3) the sensitivity of the residual to the fault is enhanced by means of a maximized
$H_-$
-norm. With the aid of the generalized Kalman–Yakubovich–Popov lemma, the mixed
$H_-/H_{\infty}$
performance and the
$D$
-stability requirement are guaranteed by solving a convex optimization problem. An iterative algorithm for designing the desired FD filter is proposed by evaluating the threshold on the generated residual function. A simulation result is exploited to illustrate the effectiveness of the proposed design technique.