Stabilization of a chain of three integrators by a feedback in the form of nested saturators

The problem of stabilizing a chain of three integrators subject to a phase constraint by a continuous constrained control is considered. The application of a feedback in the form of nested saturators results in study of a switching system. Necessary conditions of local stability are established. A Lyapunov function is constructed by means of which it is proved that the necessary conditions are sufficient for global stability of the closed-loop system. The discussion is illustrated by numerical examples.