Unknown inputs functional observers designs for delay descriptor systems

New time and frequency domain designs of unknown inputs functional observers (UIFO) for a class of descriptor systems with a constant time delay are investigated in this paper. The unknown inputs are present in both the state and the measurement equations. The time procedure design is based on the unbiasedness of the estimation error and the Lyapunov Krasovskii stability theory. After given the existence condition of such observers, the gain implemented in the functional observer with internal delay design is obtained in terms of linear matrix inequalities. The particular cases, where the observer is independent of internal delay and where it is independent of delay are also investigated. A design algorithm that summarises the different steps of the UIFO design is proposed. Then, the frequency procedure design is derived from time domain results by applying the factorisation approach, where we define some useful matrix fraction descriptions. Note that the order of this unknown input observers is equal to the dimension of the vector to be estimated. A numerical example is given to illustrate the effectiveness of the presented approach.