On an optimal choice of input for the identification of continuous-time transfer functions

Abstract

In this paper, we present an optimal input design method for the identification of single input single output continuous-time transfer functions. As a criterion of optimality, singular values of a data matrix, which represents the input-output relation of the transfer function in the kernel form, are used. If an input maximizes the second smallest singular value, the distance between signal space arid noise space is maximum, and the input is regarded as optimal. In the proposed algorithm, we show that this optimal input design problem can be rewritten as that for discrete-time systems proposed by Antoulas et al. [A.C. Antoulas et al .1999], [A.C. Antoulas, 1997], [A.C. Antoulas et al., 1998], if the input is approximated by the finite Fourier series expansion. Through numerical examples, its effectiveness is verified.