Robust H−/H∞ fault detection observer design for polytopic spatially interconnected systems over finite frequency domain

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Abstract
Summary: This article aims at solving the problem of robust H−/H∞ fault detection (FD) over finite frequency domain for spatially interconnected systems (SISs) with polytopic uncertainties. A fault detection observer is designed to generate the residual signal, and in order for the observer to work, the well‐posedness, robust stability, and finite frequency H−/H∞ indexes are properly defined for the error systems. A sufficient condition for the well‐posedness and robust stability of error systems is given based on the theory of continuous semigroup. Then, to obtain the H−/H∞ performance indexes conditions, a reformed generalized Kalman‐Yakubovich‐Popov (GKYP) lemma for polytopic SISs is derived, which takes the noncasual structure of SISs into account. It turns out that the reformed GKYP lemma is an extension of some existing results in traditional multidimensional casual systems. By resorting to Finsler's lemma and a linearization technique, the existence conditions of finite frequency H−/H∞ FD observer for polytopic SISs are given in terms of linear matrix inequalities. An illustrative example is given to demonstrate the effectiveness of the proposed method.

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