Identifiability and excitation of polynomial systems

This paper establishes identifiability and informativity conditions for a class of deterministic linearly parametrized polynomial systems. The class considered is polynomial in the states and in the inputs. The standard definitions of identifiability and informativity for linear systems are expanded to account for the situation 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, respectively on the input, to produce an informative experiment.