Mixed \(\mathcal H_2/\mathcal H_{\infty}\) approach to fault detection of discrete linear repetitive processes. (English) Zbl 1208.94032

Summary: 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 \(\mathcal H_2/\mathcal H_{\infty}\) 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 \(\mathcal H_2/\mathcal H_{\infty}\) 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.


94A13 Detection theory in information and communication theory
93E10 Estimation and detection in stochastic control theory
93B36 \(H^\infty\)-control
93C95 Application models in control theory
Full Text: DOI


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