Properties of Simple and Generalized Laguerre Functions for Time-delay System Approximations

Abstract

The properties of the simple and generalized Laguerre functions for time-invariant system approximations are discussed. The expressions for these functions are presented and the differences between them are shown. The approximations heavily depend on the free parameters of the Laguerre functions. Because of this, the optimal choice of these parameters is described for both the simple and the generalized functions. This assures that the results are satisfactory. The approximations are shown on two different systems. These approximations are evaluated with the help of the quadratic error criterion. It is shown that the results differ for the two chosen systems. The reason behind this is explained with the help of the Laguerre functions' properties and the initial value theorem.

Keywords

• Laguerre functions
• time-delay system
• system approximation
• optimal free parameters
• impulse response
• transfer function