A new parametrisation of matrix fraction descriptions to improve gradient-based optimisation methods

A new parametrisation of matrix fraction descriptions, named fully-parametrised left matrix fraction description (F-LMFD) is introduced in this article. This one contains n_y² over-parameters and consequently does not uniquely define a transfer function. Based on a study of the spanned equivalence class, local parametrisations of F-LMFD are then proposed to reduce the search space dimension when a gradient-based optimisation is performed. The formulation of the Gauss-Newton method is then considered and the new convergence scheme based on these local parametrisations is given. This one has a better numerical conditioning and is shown to avoid the numerical locking that can occurs with the conventional convergence schemes, based on minimal parametrisations of LMFD. The improvement of the convergence of the Gauss-Newton method is illustrated with the identification of a shaker.