Finite-frequency fault detection for two-dimensional Fornasini-Marchesini dynamical systems

This paper is concerned with the fault detection problem for two-dimensional (2-D) discrete-time systems described by the Fornasini-Marchesini local state-space model. The goal of the paper is to design a fault detection filter to detect the occurrence of faults in finite-frequency domain. To this end, a finite-frequency H-index is used to describe fault sensitivity performance, and a finite-frequency H-infinity index is used to describe disturbance attenuation performance. In light of the generalised Kalman-Yakubovich-Popov lemma for 2-D systems and matrix inequality techniques, convex conditions are derived for this fault detection problem. Based on these conditions, a numerical algorithm is put forward to construct a desired fault detection filter. Finally, a numerical example and an industrial example are given to illustrate the effectiveness of the proposed algorithm.