An unified formalism based on gain switching for second order sliding mode control

In this paper, an unified formalism using gain switching is proposed, thanks to which some second order sliding mode control laws can be rewritten. Indeed, three second order sliding mode control laws, including the twisting algorithm, a second order sliding mode output feedback control and a very recent output feedback control (called "twisting-like"), are presented and written under a similar formalism. Then, convergence analysis is made for these three control laws by proposing a new theorem for the convergence condition. Finally, a comparison of the three control laws performances is made through an academic example.