Stabilization of a Chain of Three Integrators by 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 feedback in the form of nested saturators results in the study of a switching system. The 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 the global stability of the closed-loop system. The discussion is illustrated by numerical examples.