This paper deals with the problem of full-order observers design for linear continuous delayed state and inputs systems with unknown input (UI) and time-varying delays. A method to design an Unknown Input Observer (UIO) for such systems is proposed based on a delay-dependent stability conditions of the state estimation error system. A Fault Detection and Isolation (FDI) scheme using a bank of such UIO, is also presented and tested on a (FDI) problem related to irrigation canals.