Explicit formulas for Hankel norm approximations of infinite-dimensional systems

Recently Hankel norm approximation for finite dimensional systems has been studied extensively, both for continuous time systems and discrete time systems. One of the approaches is to combine the work of J.A. Ball and J.W. Helton with results on Wiener-Hopf factorization to produce explicit formulas for the solutions. This has been done by J.A. Ball and A.C.M. Ran for the finite-dimensional case and for a class of infinite-dimensional systems by A.C.M. Ran. Here we show that this approach can be extended to a much larger class of infinite-dimensional systems; those with an exponentially stable semigroup and unbounded input and output operators which satisfy a smoothness condition. This class is larger than the nuclear class for which this problem was solved by K. Glover, R.F. Curtain and J.R. Partington by an approximation approach.