Necessary and sufficient condition for the existence of a proper solution to the exact model matching problem for linear time-varying systems

The exact model matching problem is formulated and studied for linear time-varying systems. The condition for the existence of a proper solution, which is well known in the time-invariant case, is proven here to be still valid in the time-varying case. The properness is characterized using the Smith-McMillan form at infinity, recently defined by the authors for the transfer matrices with time-varying coefficients.