Approximation of Irrational Matrix Functions and Its Application to Continuous-Discrete Model Conversion

Abstract

In this paper, an improved method of rational approximation is presented for evaluating the irrational matrix function f(A ), where A is a square matrix and f(s) is a scalar irrational function which is analytic on the spectrum of A . The improvement in the accuracy of the approximation off (A ) by a rational matrix function is achieved by using the multipoint Pade approximants to f(s). An application example to model conversion involving the evaluations of the matrix exponential exp (A T) and the matrix logarithm ln(F ) is provided to illustrate the superiority of the method.