Design of unknown input observer with H_∞ performance for linear time-delay systems

A unknown input observer (UIO) design for a class of linear time-delay systems when the observer error can't completely decouple from unknown input is dealt with. A sufficient condition to its existence is presented based on Lyapunov stability method. Design problem of the proposed observer is formulated in term of linear matrix inequalities. Two design problems of the observer with internal delay and without internal delay are formulated. Based on H_∞ control theory in time-delay systems, the proposed observer is designed in term of linear matrix inequalities (LMI). A design algorithm is proposed. The effective of the proposed approach is illustrated by a numerical example.