Stabilization of nonlinear systems based on robust control Lyapunov function

This paper deals with the robust stabilization problem for a class of nonlinear systems with structural uncertainty.Based on robust control l.yapunov function,a sufficient and necessary condition for a function to be a robust control Lyapunov function is given.From this condition,simply sufficient condition for the robust stabilization(robust practical stabilization)is deduced.Moreover,if the equilibrium of the closed-loop system is u-nique,the existence of such a robust control l.yapunov function will also imply robustly globally asymptotical stabilization.Then a continuous state feedback law can be constructed explicitly.The simulation shows the effectiveness of the method.

This paper deals with the robust stabilization problem for a class of nonlinear systems with structural uncertainty. Based on robust control Lyapunov function, a sufficient and necessary condition for a function to be a robust control Lyapunov function is given. From this condition, simply sufficient condition for the robust stabilization （robust practical stabilization） is deduced. Moreover, if the equilibrium of the closed-loop system is unique, the existence of such a robust control Lyapunnv function will also imply robustly globally asymptotical stabilization. Then a continuous state feedback law can be constructed explicitly. The simulation shows the effectiveness of the method.