L∞ Time-delay Unknown Input Set-membership Observer-based Actuator Fault Detection for Discrete System with Uncertainties

This paper focuses on the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$L_{\infty}$</tex> time-delay unknown input set-membership observer-based actuator fault detection problem for discrete system. In order to make fault detection robust to uncertainties including unknown interference and modelling errors, <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$L_{\infty}$</tex> performance index is employed in designing the novel observer. Moreover, the observer conditions are converted into an optimization problem constrained by linear matrix inequalities. Under the assumption that uncertainties are unknown but bounded by zonotopes, an actuator fault detection scheme based on accurate residual thresholds estimated by a zonotope set-membership approach is established. Finally, a numerical is provided to demonstrate the effectiveness of the proposed scheme.