Stabilization of Nonlinear Systems with Norm Bounded Uncertainties

In this paper, we give a necessary and sufficient condition in terms of Hamilton-Jacobi inequalities for globally stabilizing a nonlinear system, robustly with respect to unstructured uncertainties, depending both on unknown time-varying parameters Δ(t) and state x and norm-bounded for each x. This condition essentially states that global robust stabilization via smooth (except possibly at the origin) controllers is equivalent to the existence of a robust control Lyapunov function, which requires the solution of a suitable Hamilton Jacobi inequality, and generalizes a well-known condition for linear systems. This clarifies also the connection between robust stabilization and H∞ control for nonlinear systems.