The stability of solutions for non-linear control systems in the entire phase space is investigated. It is shown that for determining the global stability of motion, it is necessary to first obtain a single scalar equation from the specified system, and only then apply the Hurwitz conditions. In the derived scalar equations corresponding to the initial system, both non-linear functions and their derivatives will be present. Therefore, not only do the non-linear functions, but also their derivatives enter in the conditions for ensuring stability of the solutions in the entire phase space. Examples are given to illustrate the procedure