Robust Backstepping Control for Nonvanishing Parametrization$^1$

In this paper, a design method of a controller is presented for a class of nonlinear systems which have time-varying parametric uncertainly. Some features of this controller are that it can tackle 1) nonlinear parametrization(i.e. uncertain parameters enter the system in the nonlinear form) and 2) nonvanishing peturbation (i.e. uncertainty need not vanish at the origin). The class of systems considered in this paper has the triangular structure for which the well-known backstepping design can be applied. The uncertain parameter is assumed to be contained in the bounded set whose size can be arbitrarily large. Also, the uncertain system are globally uniformly bounded and converge to a compact set whose size is designable. In particular, the first state of the system can be made arbitrarily small, which can be seen by the presented simulation result.