The techniques described in this paper permit a universal approach to the synthesis of continuous, and sampled-data systems. Numerical methods are presented for the computation of root locus plots, transient responses, and z transforms from the block diagrams of transfer functions. These methods are for use with high-speed, general purpose, digital computers such as the IBM 7090 data processing system. The methods require little or no algebraic manipulation of system equations, even for complex multiloop systems containing both continuous and sampled-data transfer functions. Examples are given showing the use of these methods, and the results obtained. Programming details, which might be of value to persons desiring to develop similar programs, are briefly covered; future planned work and possible activities are described.