Correction to the Unknown Input Observer Design for Linear Fractional-Order Time-Delay Systems & a New Enhanced LMI Condition

Abstract

This note considers the work entitled “Unknown Input Observer Design for Linear Fractional-Order Time-Delay Systems”. In the above paper [1], the authors gave the existence conditions of such observer, then based on the fractional order Lyapunov stability approach, a sufficient condition for the asymptotic stability of the estimation error have given in a linear matrix inequality (LMI) formulation which is incorrect. In this note, we give the correction of Theorem 7. The new proposed Theorem can be applied to a large kind of delayed fractional-order-system when the delay is time varying or constant, while the above mentioned paper consider only a constant time delay. The proof is based on the diffusive representation of the fractional order derivative and the indirect Lyapunov approach proposed in [2].