@article {51,
	title = {Stability preserving maps for finite-time convergence: Super-twisting sliding-mode algorithm},
	journal = {Automatica},
	volume = {49},
	year = {2013},
	pages = {534 - 539},
	abstract = {<p>The super-twisting algorithm (STA) has become the prototype of second-order sliding mode algorithm. It achieves finite time convergence by means of a continuous action, without using information about derivatives of the sliding constraint. Thus, chattering associated to traditional sliding-mode observers and controllers is reduced. The stability and finite-time convergence analysis have been jointly addressed from different points of view, most of them based on the use of scaling symmetries (homogeneity), or non-smooth Lyapunov functions. Departing from these approaches, in this contribution we decouple the stability analysis problem from that of finite-time convergence. A nonlinear change of coordinates and a time-scaling are used. In the new coordinates and time{\^a}{\texteuro}{\textquotedblleft}space, the transformed system is stabilized using any appropriate standard design method. Conditions under which the combination of the nonlinear coordinates transformation and the time-scaling is a stability preserving map are given. Provided convergence in the transformed space is faster than O(1/T) -where T is the transformed time- convergence of the original system takes place in finite-time. The method is illustrated by designing a generalized super-twisting observer able to cope with a broad class of perturbations.</p>
},
	keywords = {Bioprocess control},
	issn = {0967-0661},
	doi = {http://dx.doi.org/10.1016/j.conengprac.2013.03.003},
	url = {http://www.sciencedirect.com/science/article/pii/S0967066113000488},
	author = {Pic{\'o}, Jes{\'u}s and Pic{\'o}-Marco, Enric and Vignoni, Alejandro and De Battista, Hern{\'a}n}
}
