In this paper, a unified solution of Hankel norm approximation problem is proposed by $delta$-operator. To derive the main result, all-pass property is derived from the inner and co-inner property in the $delta$-domain. The solution of all-pass becomes an optimal Hankel norm approximation problem in .delta.-domain through LLFT(Low Linear Fractional Transformation) inserting feedback term $phi(gamma)$, which is a free design parameter, to hold the error bound desired against the variance between the original model and the solution of Hankel norm approximation problem. The proposed solution does not only cover continuous and discrete ones depending on sampling interval but also plays a key role in robust control and model reduction problem. The verification of the proposed solution is exemplified via simulation for the zero-order Hankel norm approximation problem and the model reduction problem applied to a 16th order MIMO system.