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An algebraic state estimation approach for a class of linear time-delay system

This note provides a new algebraic method to the state estimation of linear time-delay systems. The discussed estimation technique, which is based upon standard mathematics tools of operational calculus and distribution theory, etc., is non-asymptotic. The exact formulas of the state variables in expression of the integrals of the input variable and the output variable are given in finite time to get the fast estimation. The effectiveness and performances of the proposed approach are validated by numerical examples and simulations.