The robust stabilization for nonlinear uncertain systems and H-J-I differential inequality

The robust stabilization for a class of nonlinear uncertain systems with norm-bounded time-varying uncertainty is considered. The concept of robust stabilization in the sense of Lyapunov is defined. The necessary and sufficient conditions which the robust stabilization of the systems is solvable are derived. The result shows that the robust stabilizability for a class of uncertain systems with norm-bounded uncertainties is equivalent to the existence of positive solution for an extended Hamilton-Jacobi-Isaacs (H-J-I) differential inequality