Unified Hankel Norm Approximations Using The Divided Difference Operator

A new unified solution to the optimal Hankel norm approximation is suggested using the divided difference operator. This solution unifies known continuous and discrete time solutions and inherits the numerical robustness of the divided difference operator. Further, a new parallel solution is found in the discrete time case. It is argued that one solution is better for low frequency behaviour while the other is better for high frequency behaviour. The two solutions are then shown to asymptotically approach a single continuous time solution as the sampling interval decreases to zero. Existing techniques in the literature are shown to be special cases of the new unified solution.