Normalized coprime representations for time-varying linear systems

By considering the behaviour of stabilizable and detectable, linear time-varying state-space models over doubly-infinite continuous time, we establish the existence of so-called normalized coprime representations for the system graphs; that is, stable and stably left (resp. right) invertible, image (resp. kernel) representations that are normalized with respect to the inner product on L²(-∞,∞); this is consistent with the notion of normalization used in the time-invariant setting. The approach is constructive, involving the solution of time-varying differential Riccati equations with single-point boundary conditions at either +∞ or -∞. The contribution lies in accommodating state-space models that may not define an exponential dichotomy.