•A new direct discrete model approximation based internal model controller design is proposed.•Proposed scheme is validated on the single-input single-output and the multi-input multi-output discrete dynamical models.•A robust study of proposed discrete approximation based internal model controller is demonstrated on supersonic jet engine.•Effectiveness of the proposed design methodology is illustrated through a single machine infinite bus power system. In this paper, a new direct discrete approximation based internal model control design is proposed to the linear discrete dynamical systems. The approximation method is used to determine an accurate and stable reduced-order model for the considered original higher-order discrete-time system. The method involves an enhanced Differential Evolution algorithm to ascertain the stable denominator polynomial coefficients, and the preferable reduced numerator polynomial coefficients are evaluated by using the improved discrete multi-point Padé approximation approach. The method deploys on discrete step integral square error minimization between the original dynamical system and the approximated model, together with retaining their discrete impulse response energy values. The approximated model has been considered an internal (predictive) model and proceeds with an optimal internal model controller design to improve the discrete dynamical system behaviour according to the reference input/the set point. The controller's best performance is attained by tuning the single filter parameter ′λ′ by minimizing the integral square error between the reference input and the actual output of the dynamical system using the enhanced differential evolution algorithm. The acceptability and applicability of the proposed process reduction-based controller design have been validated on a single-input single-output supersonic jet engine inlet dynamical model. The controller robust study is conducted by inserting 10% disruption uncertainty in the system dynamical model poles and zeros. The method has also been extended to the discrete multi-input multi-output dynamical model of the single machine infinite bus power system to develop an optimal internal model control-based power system stabilizer. The simulation results showing better reference input tracking, comparison of performance indices, and also highlight the efficacy of the proposed controller design.