The paper addresses problems of numerical conditioning of the discrete-time H-infinity control design based on a J-lossless coprime factorisations of a chain-scattering description of a controlled plant. it is demonstrated that forward shift operator techniques for solving the design problem may become ill-conditioned for a sufficiently small sampling period. It is shown that numerical robustness and reliability of computations can be significantly improved via utilising a so-called delta operator form of the origin problem. State space formulae for all delta-domain controllers are given. The solution is obtained via solving two coupled Riccati equations leading to J-lossless coprime factorisations of a chain scattering description of a controlled plant. In order to evaluate a measure of numerical conditioning of these solutions the relative condition number of the delta-domain algebraic Riccati equation is introduced. An example dealing with a problem of mixed sensitivity H-infinity design is given to illustrate the method.