Fault Detection Filter Design With Optimization and Partial Decoupling

For the fault detection filter design of linear time-invariant systems, we propose a novel problem formulation, which not only makes a tradeoff between fault sensitivity and disturbance sensitivity, but also incorporates partial fault decoupling and disturbance decoupling. This formulation compensates the drawbacks of the available frameworks such as H
_-
/H
_∞
, H
₂
/H
_∞
and H
_∞
/H
_∞
. One optimal fault detection filter design for this problem framework is derived. It is shown that the faults in a certain space have arbitrary sensitivities, while the faults in the complementary space have bounded and maximized sensitivities with the proposed filter. Both the decoupling and non-decoupling conditions are derived. Moreover, decoupling disturbances is discussed. Finally, an example is given to illustrate the results.