A note on a minimum detectable actuator fault of dynamic systems under ellipsoidal bounding

The paper deals with the estimation of actuator faults for dynamic systems along with assessing their uncertainty. In particular, it is assumed that the external disturbances are bounded within an ellipsoidal domain. For the purpose of further deliberations, $\mathcal{H}_{\infty}$ performance is also imposed. As a result, a set of complementary fault uncertainty intervals is obtained, which are minimised in such a way as to obtain a minimum detectable actuator fault. The final part of the paper show a numerical example concerning fault estimation of a multi-tank system.