In this paper, a novel systematic method for the polynomial controllers (denoted as RST controllers) design and tuning is proposed and successfully implemented based on an epsilon-multiobjective particle swarm optimization (ε-MOPSO) algorithm. The ε-domination concept is used to further improve both properties of the non-premature convergence towards Pareto-optimal sets and the diversity among the found solutions. The RST polynomials coefficients’ computation is formulated as a constrained multiobjective optimization problem under operational frequency-domain constraints. The proposed methodology aims to optimize a desired output sensitivity function satisfying nominal performance and H∞ robustness specifications of the closed-loop system. The use of a suitable fixed parts of the optimized output sensitivity function will provide partial poles placement of the closed-loop dynamics. The inverse of such an optimized desired sensitivity function defines the performance and robustness H∞ weighting filter. Such a proposed ε-MOPSO algorithm is firstly compared with several homologous MOPSO, non-dominated sorting genetic algorithm II (NSGA-II) and multiobjective differential evolution (MODE) algorithms for a benchmark of multiobjective test functions. The algorithms’ performances are evaluated in terms of several metrics in order to show the superiority and the effectiveness of the proposed method. An application to the axis position control of a flexible transmission system with varying loads is then performed. Demonstrative simulations are carried out to show the remarkable superiority and effectiveness of the proposed ε-MOPSO-tuned digital RST controllers compared with several well-known methods available in the literature.