  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.
