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Finite dimensional Laguerre polynomial expansion can be applied to approximate the solution of linear time-invariant systems. Here, we extend this approach to systems with small time delay by introducing a delay matrix operator to the system equations. In addition, parameters of linear unity-feedback systems with small time delay can also be estimated by using the Laguerre expansion. In this paper we provide algorithms for large scale systems to avoid direct matrix inversion and give examples to demonstrate the approximation.

The elements of the observer matrix are determined to meet the specified eigenvalues, distinct and multiple, and at the same time, the measure of quadratic estimate error expressed in block pulse functions is minimized. It is relatively simple as compared to other design methods for optimal observers.

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