Singularity of backstepping control for non-linear systems

The backstepping procedure is one of the tools, which provides control law synthesis for non-linear smooth systems. Two classes of non-linear systems are usually considered. The first group is the so called strict-feedback systems and the second, more general, pure-feedback systems. The backstepping procedure applied to pure-feedback systems results sometimes in a control law, which exhibits singularity. In the paper an intermediate class of non-linear systems is described. It is much broader than strict-feedback systems, but it is assured that derived control law is numerically well posed. Such a class of systems is important in thermal plants, where flow of fluids occur.