Variable structure control of systems with uncertain nonlinear friction (Q1614382)

A single-input single-output control system is considered in the presence of bounded uncertain, possibly non-smooth, nonlinearities (such as a friction). A multi-state backstepping procedure for variable structure control design is proposed. It is proved that the resulting feedback control is smoothed and steers the state into a neighbourhood of the origin, the size of which shrinks with the design (smoothing) parameter \(\varepsilon\). An illustrative example (a model of a motor-load drive system) is considered, and some simulation results are presented.