FINAL VERSION 1 On Design of Robust Fault Detection Filter in Finite Frequency Domain with Regional Pole Assignment

Abstract—This paper is concerned with the fault detection filter design problem for uncertain linear discrete-time system in finite-frequency domain with regional pole assignment. An optimized fault detection filter is designed such that 1) the fault detection dynamics is quadratically D-stable; 2) the effect from the exogenous disturbance on the residual is attenuated with respect to a minimized H∞-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 ∞ performance and the D-stability requirement are guaranteed by solving a convex optimization problem. An iterative algorithm for designing the desired fault detection 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. Index Terms—Fault detection filter, regional pole assignment, finite frequency domain, parameter uncertainties, GKYP lemma. I