Design of full order unknown input observers for delayed singular systems with state variable time delay

In this paper, we propose a new time-domain design of an Unknown Input Full Order Observer (UIFOO). The considered systems are delayed singular ones with known and unknown inputs. The time delay are of two kinds. The state delay is variable but the known input delay can be variable or constant. The proposed approach is based on the unbiasedness of the estimation error and Lyapunov-Krasovskii stability theory. The observer optimal gain satisfies a sufficient condition of the observer stability dependent on the state delay. This condition is expressed in term of Linear Matrix Inequalities (LMIs) formulation.