An optimization approach for the design of robust discrete-time control systems is presented. Using pole clustering, the design specifications for the system time response are recast in the form of inequality constraints governing the free design parameters. Quantitative robustness and disturbance rejection measures are discussed using Lyapunov matrix equations. A performance index combining the robustness and disturbance rejection measures is minimized subject to the parameter inequality constraints to obtain the desired design. A numerical example is given to illustrate the usefulness of the design approach.