On an optimal input design for the 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 the optimality, the singular values of a data matrix representing the input-output relation of the considered system are used. An input maximizing the second smallest singular value is regarded as optimal because the distance between the signal space and the noise space is maximized. It is shown that if the input is approximated by the finite Fourier series expansion this optimal input design problem can be rewritten as the problem for discrete-time systems proposed by Antoulas et al.(1)) Through numerical examples, the effectiveness is shown and verified.