Least-Squares Estimator for Hereditary Systems with Time-Varying Delay

A constructive solution to the estimation problem of linear hereditary systems with time-varying delay is presented using a least-squares fit to the contaminated data. The utilization of optimum control theory yields a split boundary value problem, which is transformed to an initial-value problem by utilizing the theory of Fredholm resolvents. Applications of the theory to man-machine systems, for example, are indicated.