On The Design of a reduced order H∞ filter for systems with unknown delay

In this note we investigate the filtering problem for linear time-delay systems. Unlike most of the existing results, we consider systems with an unknown and constant delay. From the Razumikhin stability theorem and some judicious mathematical manipulations, a reduced order H_∞ filter able to ensure the asymptotic stability and the pro-specified H_∞ performances of the filtering process is designed. Also the maximal allowable delay preserving the asymptotic stability is given. A numerical example is provided to show the effectiveness of the proposed technique.