The study of application scope for backstepping technique

The backstepping procedure is one of the tools, which provides control law synthesis for nonlinear smooth systems. A class of nonlinear systems which is so-called strict-feedback systems is usually considered, but the backstepping procedure applied to pure feedback nonlinear systems results sometimes in a control law, which exhibits singularity. In this paper, a class of pure nonlinear systems which satisfies some given sufficient conditions is described, and the derived control law is numerically well posed. Another class of systems which has weakened conditions than above discussed systems is also considered which makes the application scope of backstepping technique more extensive. The simulation results demonstrate that the control law of this class of systems does not exhibit singularity, which means division by zero or ill-conditioned.