Robust stabilization of nonlinear systems with pointwise norm bounded uncertainties: a control Lyapunov function approach

In this paper, the authors give a necessary and sufficient condition for globally stabilizing a nonlinear system, robustly with respect to unstructured uncertainties ( ~ u; x; t); norm-bounded for each fixed x and u: This condition requires one to find a smooth, proper, and positive definite solution V (x) of a suitable partial differential inequality depending only on the system data. A procedure, based on the knowledge of V (x); is outlined for constructing almost smooth robustly stabilizing controllers. Our approach, based on Lyapunov functions, generalizes previous results for linear uncertain systems and establishes a precise connection between robust stabilization, on one hand, and H1-control sector conditions and input-to-state stabilization on the other.