On an Optimal Choice of Input for Identification of Continuous-time Transfer Functions

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 a transfer function, are used. If an input maximizes the second smallest singular value of a data matrix contaminated by noise, the noise-contaminated data matrix most accurately approximates a noise-free data matrix. Thus the input can be regarded as an optimal input in that sense. The formulation of this optimal input design problem becomes similar to that for discrete-time systems proposed by Antoulas et al. [1, 2, 3], if the input is approximated by the finite Fourier series expansion. Through numerical examples, its effectiveness is verified.