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In this paper a strong Lyapunov function is obtained, for the first time, for the supertwisting algorithm, an important class of second order sliding modes (SOSM). This algorithm is widely used in the sliding modes literature to design controllers, observers and exact differentiators. The introduction of a Lyapunov function allows not only to study more(More)
Resumen— A second order sliding mode controller, the so-called " Twisting " algorithm is under study. A non-smooth strict Lyapunov function is proposed, so global finite time stability for this algorithm can be proved, even in the case when it is affected by bounded external perturbations. The strict Lyapunov function gives the possibility to estimate an(More)
An arbitrary order differentiator that, in the absence of noise, converges to the true derivatives of the signal after a finite time independent of the initial differentiator error is presented. The only assumption on a signal to be differentiated (n − 1)-times is that its n-th derivative is uniformly bounded by a known constant. The proposed differentiator(More)
Resumen— Observation problem for systems governed by Partial Differential Equations (PDE) has been a research eld of its own for a long time. In this paper it is presented an observer design for a class or parabolic PDE's using sliding modes theory and bacstepping-like procedure in order to achieve exponential convergence. A Volterra-like integral(More)
The operation of a sequencing batch reactor (SBR) exposed to high concentration peaks (shock loads) of a toxic compound (4-chlorophenol, 4CP) was evaluated. Two control strategies based on on-line measurements of the dissolved oxygen concentration were tested. The first strategy, called variable timing control (VTC), detects the end of the reaction period(More)
—The differentiators based on the Super-Twisting Algorithm (STA) yield finite-time and theoretically exact convergence to the derivative of the input signal, whenever this derivative is Lipschitz. However, the convergence time grows unboundedly when the initial conditions of the differentiation error grow. In this paper a Uniform Robust Exact Differentiator(More)