Construction of a Lyapunov Function for Nonlinear Cascaded Systems with Dynamic Uncertainties

The global robust stabilization problem of cascaded systems with dynamic uncertainties has been approached by the small gain theorem. This method, however, does not produce an explicit Lyapunov function for the closed-loop system. In this paper, we develop a Lyapunov direct method based recursive approach to solve the global robust stabilization problem for the said systems. This method is not only more straightforward than the small gain method, but also produces an explicit Lyapunov function for the closed-loop systems. The Lyapunov function is indispensable when the adaptive control of the same class of systems is further considered