Joint Observer Gain and Input Design for Asymptotic Active Fault Diagnosis

This paper proposes a joint gain and input design method for observer-based asymptotic active fault diagnosis, which is based on a newly-defined notion named the excluding degree of the origin from a zonotope. Using the excluding degree, a quantitative specification is obtained to characterize the performance of set-based robust fault diagnosis. Furthermore, a single gain design method and a joint gain and input design method are proposed, respectively. This is the first work to achieve a joint observer gain and input design for set-based active fault diagnosis. Compared with the existing methods that design gains and input separately, the proposed joint gain and input design method has advantages to exploit the fault diagnosis potential of observer-based schemes. Finally, several examples are used to illustrate the effectiveness of the proposed methods.