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A maximum speed of response control of switches-based system described by a second-order difference equation is proposed. A feedback is produced as a linear combination of the differences of system variables. The equation is transformed to the form with nilpotent matrix. The solution of the transformed difference equation converges into a fixed point after two steps. The equation is transformed with the help of a special matrix. The two matrix elements representing the multipliers at the differences of variables are determined. Depending on the loci of the elements in the matrix, the problem of their calculation is formulated as linear or non-linear. Its solution gives the two functions of elements of the matrix of difference equation. Variation of the elements leads to corresponding changes of multipliers and, as a result, a convergence of transient into a fixed point within two steps remains as well. The control principle proposed can provide a theoretical basis for developing switches-based systems with maximum possible dynamic behavior in the single point of nominal operating mode as well as in the region of parameters. The example of synthesis a control of pulse-width converter used for current regulation in active-inductive load is resulted, which demonstrates significantly improvement of system dynamic behavior.