A New Functional Observer Design of linear Singular Systems with an additional unknown input and variable time delay in Time and Frequency domains

In this paper, we propose both time and frequency domain design of an Unknown Input Functional Observer for linear singular systems with variable time delays injected into the state and the input vectors. This technique provides also an estimation of the unknown input existing on state and output equations. The design procedure is obtained by considering time domain solution, based on Lyapunov-Krasovskii stability theory. The proposed observer is characterized by a gain which is the solution of Linear Matrix Inequalities (LMI) conditions. The frequency procedure design is derived from time domain results by using the coprime factorization approach. We propose, also, a numerical example to illustrate the effectiveness of the proposed approach.