Identifiability and excitation of linearly parametrized rational systems

This paper establishes identifiability and informativity conditions for a class of deterministic linearly parametrized rational models. The class considered is rational in the states and polynomial in the inputs. The standard definitions of identifiability and informativity for linear systems are expanded to account for the situation, common for nonlinear deterministic systems, where the identification is achieved either through the application of informative inputs or via the response to informative initial conditions. We provide necessary and sufficient conditions for identifiability from the initial state, respectively from the input, as well as necessary and sufficient conditions on the initial state to produce an informative experiment. We also provide sufficient conditions on the input to be informative when the initial condition is unknown and could therefore potentially destroy the transfer of information from the input to the regressor.