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 gl obally stabilizing a nonlinear system, robustly with respect to unstructure d uncertainties <(Phi)over tilde>(u,x,t). norm-bounded for each fixed x and u. This condition requires one to find a smooth, proper, and positive defi nite 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 o utlined for constructing almost smooth robustly stabilizing controllers. Ou r approach, based on Lyapunov functions, generalizes previous results for l inear uncertain systems and establishes a precise connection between robust stabilization, on one hand, and H-infinity-control sector conditions and i nput-to-state stabilization on the other.