H-/L∞ UIO-Based Robust Fault Diagnosis Design in Finite Frequency Domain for Discrete-Time Systems

Abstract

This study investigates the problem of robust fault diagnosis for discrete-time systems subjected to actuator faults and unknown input disturbances. A novel <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$H-/L_{\infty}$</tex> unknown input observer (UIO) based on the generalized Kalman-Yakubovich-Popov (GKYP) lemma is presented by decoupling the partial unknown input disturbances and attenuating the unknown input disturbances that cannot be decoupled. Then, the H- performance index in the finite frequency domain is used to measure the fault sensitivity and the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$L_{\infty}$</tex> performance index is used to reduce the influence of unknown input disturbances on fault diagnosis results and ensure the robustness performance. A residual evaluation function and a time-varying threshold are presented based on the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$L_{\alpha}$</tex> performance index. In addition, sufficient conditions for designing the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$H-/L_{\infty}$</tex> UIO are proposed and transformed into linear matrix inequalities (LMIs) that can be easily solved. Finally, simulations of a simple discrete-time system are used to validate the effectiveness of the developed <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$H-/L_{\infty}$</tex> UIO.