A note on continuous delayed sliding mode control

A new continuous sliding mode control approach is introduced with the dedicated mathematical tools. A time-delay modification/approximation of sign function is proposed, and it is shown that by substituting this new “sign” realization in the conventional sliding mode algorithms the main advantages of the sliding mode tools are preserved (like time of convergence and uniformity of stability with respect to matched disturbances), while the chattering is seriously reduced. These results are illustrated and confirmed by numerical simulations for the first order sliding mode control and the super-twisting algorithm.