Global Stability of the Solutions of Nonlinear Control Systems

This paper deals with the stability of solutions of nonlinear control systems in the entire phase space. 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 nonlinear functions and their derivatives appear. Therefore, not only do the nonlinear 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.