Information cost for the state reconstruction of linear time invariant systems

This paper considers how much one must know, a priori, about a particular state space system to recover it from its transfer function. Knowing that one has access to full state measurements is clearly sufficient to uniquely specify a specific state space model from a given transfer function, but identifying what information is necessary for such state reconstruction is not as obvious. This work provides an exact, necessary and sufficient condition for state reconstruction, demonstrating that a priori knowledge equivalent to full state measurements is essentially necessary to recover the particular state representation generating a given transfer function. The information cost for state reconstruction is thus seen to be quite expensive for most large scale applications, motivating the need for alternative system representations that are not as structurally detailed as state space models and can be reconstructed from input-output information more easily.