Mixed H₂/H_∞ approach to fault detection of discrete linear repetitive processes

Linear repetitive processes (LRPs) are a distinct class of two-dimensional (2-D) systems, which have extensive applications in the practical industry, such as, long-wall coal cutting and metal rolling operations. This paper is concerned with the problem of mixed H2/H∞ filter design for discrete LRPs with its application to fault detection. Our attention is focused on the design of a fault-detection filter for generating a residual signal which can be processed to decide whether or not a fault has occurred in the process. A sufficient condition of the mixed H2/H∞ performance for the fault-detection process is proposed. The solvability condition for a desired fault-detection filter is also established, and the corresponding fault-detection filter design is cast into a convex optimization problem which can be efficiently handled by using the standard softwares. A numerical example is given to demonstrate the effectiveness of the proposed design procedures.