Backstepping control of a class of nonlinear systems with unknown dead-zone

In this paper, we consider the same class of systems as in X.S. Wang, et al. (2003), i.e. a class of uncertain dynamic nonlinear systems preceded by unknown dead-zone nonlinearities, in the presence of bounded external disturbances. By using backstepping technique, robust adaptive backstepping control algorithms are developed. Unlike some existing control schemes for systems with dead-zone, the developed backstepping controller do not require the uncertain parameters within known intervals. Also, no knowledge is assumed on the bound of the 'disturbance-like' term, a combination of the external disturbances and a term separated from the dead-zone model. It is shown that the proposed controllers not only can guarantee global stability, but also transient performance.