Convergence of Laguerre Impulse Response Approximation for Noninteger Order Systems

Abstract

One of the most important issues in application of noninteger order systems concerns their implementation. One of the possible approaches is the approximation of convolution operation with the impulse response of noninteger system. In this paper, new results on the Laguerre Impulse Response Approximation method are presented. Among the others, a new proof of L 1 convergence of approximation is given, allowing less strict assumptions. Additionally, more general results are given including one regarding functions that are in the joint part of L 1 and L 2 spaces. The method was also illustrated with examples of use: analysis of "fractional order lag" system, application to noninteger order filters design, and parametric optimization of fractional controllers.