Fault detection based on robust adaptive thresholds: A dynamic interval approach

Abstract

A dynamic interval approach for the fast computation of robust adaptive thresholds for a class of uncertain linear systems is the subject of this paper. An extension of recent results about the design of stable interval observers for linear systems with additive time-varying zonotopic input bounds is proposed. It allows the explicit computation of adaptive thresholds ensuring a guaranteed robustness with respect to structured and bounded disturbances which can be not only additive but also multiplicative. Moreover, the constant term (center) of the uncertain time-varying state matrix need not be diagonalizable thanks to results based on a Jordan decomposition. A sufficient condition not only ensuring the stability of the initial uncertain model but also the nondivergence of the computed adaptive thresholds is given. A numerical example dealing with fault detection in an electrical drive illustrates the proposed scheme.