In this paper the problem of stability analysis of linear closed-looped systems under interval uncertainties is considered. The problem is reduced to the problem of determining outer bounds on the ranges of the eigenvalues of interval matrices with dependent coefficients with respect to the independent elements of all other interval matrices A' , B u K. The case of real eigenvalues is discuss for simplify' the presentation. The method is suggested first for stability analysis of open linear systems under interval data. It consist of setting up and solving a system of n nonlinear equations with n unknowns with real coefficients. The latter system is only mildly nonlinear and its solution presents no numerical difficulties. An example illustrating the applicability of the method presented is provided.

A method for the synthesis of weakly nonlinear oscillators systems by using qualitative theory of differential equations analysis is proposed in this article. The self- sustained oscillations in such systems are regarded as limit cycles. The synthesis of weakly nonlinear oscillators systems possessing limit cycles with preliminarily assigned properties is done by the Melnikov function.

In the present article are proposed: structure of a fractional order control system; method for the synthesis of a fractional algorithm of a new class; method for a discretization of the fractional algorithm; it is deducated a finite difference equation suitable for a direct configuration of discrete controllers; it is submitted and solved a numerical example for the synthesis of a system with the proposed structure by using the method for the synthesis; the robust features of the synthetized system are proved.