Stabilization of a chain of exponential integrators using a strict Lyapunov function

We solve a stabilization problem for a chain of exponential integrators, using a new Matrosov type construction that provides a global strict Lyapunov function with one auxiliary function. In the suitably transformed variables, the right sides of both equations of the system saturate on the upper end at one, so the system is not completely controllable. The strictness of our Lyapunov function is key to proving input-to-state stability under additive uncertainty on the control, using a redesigned feedback control.