Global nonsmooth stabilization of a class of nonlinear cascaded systems with time-varying delay

The global nonsmooth stabilization problem for a class of nonlinear cascaded systems with time-varying delay is addressed in this paper. The control law is constructed in two steps. Firstly, by utilizing the famous homogeneous domination technique and designing appropriate Lyapunov-Krasovskii functional, a global state feedback control law is proposed for the driving subsystem; Secondly, it is proved that under suitable conditions the whole system can be globally stabilized by the proposed control law. Furthermore, a numerical example is given to illustrate the rationality and effectiveness of control scheme.