Adding an integration and global asymptotic stabilization of feedforward systems

We are concerned with systems which generalize the form x˙=h(y,u), y˙=f(y,u), where the state components x integrates functions of the others components y and the inputs u. We give sufficient conditions under which global asymptotic stabilizability of the y-subsystem (represented by saturated control) implies global asymptotic stabilizability of the overall system. This is established by an explicit Lyapunov design of the control law. We show how it serves as a basic tool to be used, may be recurrently, to deal with more complex systems. In particular the stabilization problem of the so called feedforward systems is solved this way