Robust tracking and model following of uncertain non-linear systems with time-varying delays and dead-zone inputs

The problem of robust tracking and model following is considered for a class of uncertain non-linear systems with any time-varying delays and completely unknown dead-zone input non-linearity. Here, time-varying delays are assumed to be any continuous and bounded non-negative functions, and any information on their derivatives need not known. In the study, the system uncertainties assumed to be any continuous and bounded non-linear functions, and their non-linear upper bounds do not need also to be known. Based on Wu inequality, a novel design method is presented by which some simple and direct robust tracking control schemes can be easily constructed. It is shown that the tracking error between the output of an actual dynamical system and the dynamical signals of the given reference model can be guaranteed to be uniformly exponentially bounded. A numerical example is also given to describe the design procedure of the presented method, and the simulations of this numerical example are implemented to demonstrate the validity of the theoretical results.