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This article deals with the issue of parametric synthesis of a linear controller that provides aperiodical character of transition processes. The proposed solution addresses a decomposition approach towards the parametric synthesis of linear controllers in aperiodical interval control systems. The approach relies on the division of a characteristic polynomial of a system into the dominating polynomial, provided a dominating real pole, and a free polynomial that defines the rest system poles allocation. In order to allocate the free polynomial roots at a maximum possible distance from an imaginary axis, the sufficient conditions providing a quasi-maximum degree of stability have been set. The decomposition approach in combination with these conditions has allowed developing the methodology on parametric synthesis for linear controllers providing the quasi-maximum degree of the polynomial roots domination. The methodology implementation has been carried out in practice and introduced in this paper with a numerical example.