This paper discusses the problem of synthesizing a digital dynamic controller to implement uniaxial gyrostabilizer position stabilization control in the presence of uncertain external perturbing factors. H∞ optimization is used to suppress unknown external end energy perturbations, and concepts of mixed H2/H∞ control are used to implement control in the presence of noise in the measurement channels. A H2/H∞ robust control based digital controller well proven as a means of controlling objects with parametric uncertainty, structural uncertainty, and perturbing effect uncertainty, has been selected as a controller for counterbalancing the perturbing effects. The synthesis has resulted in a digital controller effectively counterbalancing the perturbing effects upon the uniaxial gyrostabilizer