Identifiability of time-varying parameters in a class of linear dynamical systems

This paper deals with the problem of determining time-varying parameters in a system described by a linear differential equation from noise-free observations of input/output signals. For the special case of periodically varying parameters, two identifiability questions are discussed: 1) how to check whether the available experimental data allow unique determination of system parameters, and 2) how to design the experiment to accomplish this with a priori knowledge. Necessary and sufficient conditions for identifiability are obtained.