This paper establishes identifiability and informativity conditions for a class of deterministic linearly parametrized scalar rational models. The class considered is rational in the state and polynomial in the input. 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 an informative input or via the response to an informative initial condition. 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.
Gevers, M., Bazanella, A. S., Coutinho, D. F., & Dasgupta, S. (2016). Identifiability and excitation of linearly parametrized rational systems. Automatica, 63, 38–46. https://doi.org/10.1016/j.automatica.2015.10.028