Set-membership identification of continuous-time systems through model transformation

In this paper, we consider the identification of continuous-time linear-time-invariant systems from sampled input-output data corrupted by unknown but bounded noise. We formulate the problem in the framework of errors-invariables set-membership identification. First, we derive a mathematical description of the feasible parameter set in terms of polynomial constraints. Such a description accounts for a-priori information on the model structure and the noise bounds, and for the effects of the discretization error. Then, we select the parameter estimate from the feasible parameter set by computing the solution to a suitable polynomial optimization problem. We show the effectiveness of the proposed approach through a numerical example.