A New Functional Observer Design of Delayed Singular Systems in Discret-time and Frequency domains

This paper presents both discrete-time and frequency domain design of functional unknown inputs observer for discrete-time singular delayed systems. The main interest is that the proposed observer estimates a functional state and an unknown input vector. The discrete-time procedure design is based on the unbiasedness of the estimation error of the observer using Lyapunov functional. The problem is solved by means of Linear Matrix Inequalities (LMIs) to find the optimal gain implemented in the functional observer design. The frequency domain procedure design is derived from discrete-time domain results, where we propose a suitable coprime Matrix Fractions Descriptions (MFDs). A numerical example is given to prove the effectiveness of the proposed approach.