Sub-optimal Hankel norm approximation for the analytic class of infinite-dimensional systems

摘要

The sub-optimal Hankel norm approximation problem is solved under the assumptions that the system is given in terms of a triple of operators (-A, B, C), where -A is the infinitesimal generator of an exponentially stable, analytic semigroup on the Hilbert space Z, B is an element of L (C-m, Z(alpha)) where -1 < alpha less than or equal to 0, C is an element of L (Z, C-p), and the system is approximately controllable. An explicit parameterization of all solutions is obtained in terms of the system parameters -A, B, C.