Global and exact HOSM differentiator with dynamic gains for output-feedback sliding mode control

In this paper we introduce a global differentiator based on higher-order sliding modes (HOSM) and dynamic gains to solve the problem of trajectory tracking via output-feedback for a class of uncertain nonlinear plants with arbitrary relative degree and disturbances. Norm observers for the unmeasured state are employed to dominate the disturbances as well as to adapt the gains of the proposed differentiator since the nonlinearities may be state-dependent and time-varying. Uniform global stability and robust exact tracking are guaranteed employing the proposed HOSM based exact differentiator. The obtained results are not restricted to first-order sliding mode control feedback, but applies for second order sliding mode algorithms (twisting, super-twisting and variable gain super-twisting) as well as quasi-continuous HOSM finite-time controllers. Simulations with an aircraft pitch-control application illustrate the claimed properties, even in the presence of measurement noise.