A New Functional Observer Design of Delayed Systems in Time and Frequency Domains

This paper presents new time and frequency domain designs of a functional unknown input observer for a class of linear delayed systems fed by unknown input in both dynamic and output equations. In addition a comparative analysis between time domain, frequency domain based on time domain results and direct frequency domain is provided. The main interest here is to propose an observer that estimates a functional state and an unknown input vector. The time domain procedure design is based on Lyapunov-Krasovskii stability theory after giving the existence condition of such observers. The optimal gain implemented in the functional observer with internal delay design is obtained in terms of Linear Matrix Inequalities (LMIs). The frequency procedure design is derived from time domain results by applying the factorization approach where we define some useful Matrix Fraction Descriptions (MFDs). The efficiency of the proposed approach is shown by a numerical example.