Identification and state realisation of non-rational convolution models by means of diffusive representation

摘要

The authors introduce a new identification method for general causal convolution models of the form u ș2; h * u = H(Ƞ2;t)u, where h is the impulse response of the system, to be identified from measurement data. This method is based on a suitable parameterisation of operator H(Ƞ2;t) deduced from the so-called diffusive representation, devoted to state representations of such integral operators. Following this approach, the complex dynamic features of H(Ƞ2;t) can be summarised by a few numerical parameters on which the identification method will focus. The class of concerned convolution operators includes rational as well as non-rational ones, even of complex nature. For illustration, we implement this method on a numerical example.