This paper presents a novel direct form to design a digital robust control using RST structure (i.e., name given because of the R, S and T polynomials computed) based on convex optimization such as Chebyshev sphere; this approach was applied to a DC-DC Buck converter. This methodology takes into account parametric uncertainties and a Chebyshev sphere constraint in order to ensure robust performance and stability of the system in the discrete domain. For this purpose, a mathematical model for the DC-DC Buck converter is presented when considering uncertainties in electrical variables, such as load resistance, inductance, capacitance, and source voltage variation, also to obtain the discrete model of the system by using the bilinear transformation. The proposed methodology is compared with two other approaches designed in a discrete domain: the classical pole placement and the robust methodology based on the Kharitonov theorem. Wide-ranging experiments are performed in order to evaluate the behavior of the control methodologies when the system is subject to parametric variations of the load resistance and voltage setpoint variation. The results show that the proposed methodology outperforms the other approaches in 90% of the tests and ensures robust stability and robust performance when the system is subjected to a parametric uncertainties family.
