The article is devoted to the constructive study of the stabilizability of the solution of the Cauchy problem to a periodic function for system of differential equations with delay and periodic parameters. The results obtained in this paper are natural continuation of research in this area (see, for example, the works of J.S.P. Munembe). The proposed research method is based on the use of the Cauchy matrix of the system under consideration. Knowledge of the Cauchy matrix allows us to construct an auxiliary numerical matrix and reduce the problem to estimating the spectral radius of this matrix. Fulfillment of the condition that spectral radius of the specified matrix is less than one guarantees the presence of the stabilizability property.The source of the effective implementation of the proposed method for studying the problem under consideration is the possibility of accurately constructing the Cauchy matrix of a differential equation with piecewise linear delay based on the approach proposed by the author. As an illustration, the article considers an example of the Cauchy problem for a differential equation with piecewise linear delay and periodic parameters. For a given equation, the Cauchy function is constructed using precision computing software, and it is also proved that the solution of the Cauchy problem has the property of stabilizability to a periodic function

stabilizability of the solution of the Cauchy problem, differential equation with delay and periodic parameters, piecewise linear delay, constructive approach, Cauchy matrix.