Global stabilization of nonlinear cascaded systems with a Lyapunov function in superposition form

The global stabilization problem of nonlinear cascaded systems has been well studied in literature. In particular, a Lyapunov function in superposition form has been explicitly constructed for the closed-loop system in a recent paper provided the nonlinearities are polynomial. This paper removes this polynomial assumption and gives a more general result. For this purpose, a special version of changing supply function technique is utilized which preserves the superposition form of supply functions during the “changing” procedure.