A New Approach for the Design of a Functional Unknown Input Observer for Delayed Singular Systems: The Discrete Time Case

Abstract

This paper addresses the problem of a functional unknown input observer for discrete linear singular systems with variables state delay considered in the dynamic and output equations. The considered system representations are reformulated in order to develop an observer scheme independently from unknown variable delay and known input injected on the dynamic equation. The developed algorithm is based on Lyapunov-Krasovskii theory and proposes an observer gain as a solution of LMI conditions. We propose a numerical example to prove the effectiveness of our proposed approach.