Identification method for polynomially parametrized LTI systems based on exhaustive modelling with algebraic elimination

Abstract

Realization problems of impulse responses for linear time-invariant (LTI) systems are well-studied. In particular, the realizations with the least order of such systems are said to be minimal. Apart from these problems, parameter estimations of pre-defined LTI models with a specific parametrization of the system matrices are also important. In this paper, we propose a parameter estimation method for such LTI models by transforming a minimal realization obtained through black-box identifications. Our approach is based on the minimal realization theory, exhaustive modelling, and algebraic elimination. Contrary to the existing methods, the proposed method allows polynomial parametrizations of the system.