Identifiability of linear and nonlinear dynamical systems

This short paper considers the identification of dynamical systems from input-output data. The problem of parameter identifiability for such systems is approached by considering whether system outputs obtained with different parameter values can be distinguished one from another. The results are stated formally by defining the notion of "output distinguishability." Parameter identifiability is then defined precisely in terms of output distinguishability. Relationships have been developed with the other definitions such as least square identifiability and identifiability from the transfer function. Several results for linear and nonlinear systems are presented with examples.