Quasi-continuous high-order sliding-mode controllers

A universal finite-time-convergent controller is developed capable to control the output σ of any uncertain SISO system of a known permanent relative degree r. The mode σ≡0 (r-sliding mode) is established by means of a control dependent only on σ, σ, ..., σ^(r-1) and continuous everywhere except the set σ=σ=...=σ^(r-1)=0. An output-feedback controller version is also developed. With σ being the tracking deviation, the exact finite-time-convergent output tracking is provided in the absence of output noises, otherwise the tracking accuracy is proportional to the magnitude of the noise. In the latter case σ≡0 is not attained producing an unswitched control continuous in time. The resulting performance is significantly improved compared with known r-sliding controllers.