In this paper, a new sliding mode observer (SMO) for state estimation of linear systems with unknown time-varying delay, and in the presence of unknown input is presented. This method is an extension on well known unknown input SMO, proposed by Zak. In our approach, the design procedure is very simplified in comparison with the other similar SMO. With an adequate choice of a Lyapunov-Krasovskii functional, sufficient conditions are obtained in LMIs terms to guarantee asymptotic stability of the state estimation errors. In order to reach a guaranteed convergence rate, the dynamic properties of observer are also analyzed. The effectiveness, simplicity, and straight-forwardness of method are shown by simulation of a numerical example.

Keywords: Sliding Mode Observer, Time-delay, Unknown input, LMIs

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