Fault detection for discrete‐time Lipschitz non‐linear systems in finite‐frequency domain

Abstract

In this study, the problem of fault detection (FD) observer design for discrete-time Lipschitz non-linear systems with finite-frequency specifications is investigated. The finite-frequency H ∞ and H − indices are introduced to measure the robustness to unknown disturbances and the sensitivity to faults, respectively. Based on the use of a reformulated Lipschitz property, the non-linear error dynamics are transformed into a linear parameter varying (LPV) system. A new lemma is proposed to characterise the system performances in finite-frequency domain. To reduce the conservativeness of the multi-objective problem, slack variable techniques are used to obtain the sufficient conditions for the design of FD observer which are derived in terms of linear matrix inequalities (LMIs). The proposed design method can provide less restrictive LMI conditions and achieve a better FD performance than the existing one in full frequency domain. Two numerical examples are given to show the effectiveness and superiority of the new results.