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- Jorge Davila, Leonid M. Fridman, Arie Levant
- IEEE Trans. Automat. Contr.
- 2005

The super-twisting second-order sliding-mode algorithm is modified in order to design a velocity observer for uncertain mechanical systems. The finite time convergence of the observer is proved. Thus, the observer can be designed independently of the controller. A discrete version of the observer is considered and the corresponding accuracy is estimated.

- Fernando Castaños, Leonid M. Fridman
- IEEE Trans. Automat. Contr.
- 2006

The robustness properties of integral sliding-mode controllers are studied. This note shows how to select the projection matrix in such a way that the euclidean norm of the resulting perturbation is minimal. It is also shown that when the minimum is attained, the resulting perturbation is not amplified. This selection is particularly useful if integral… (More)

- Igor Boiko, Leonid M. Fridman, Alessandro Pisano, Elio Usai
- IEEE Trans. Automat. Contr.
- 2007

A systematic approach to the chattering analysis in systems with second-order sliding modes is developed. The neglected actuator dynamics is considered to be the main cause of chattering in real systems. The magnitude of oscillations in nonlinear systems with unmodeled fast nonlinear actuators driven by second-order sliding-mode control generalized… (More)

- Matteo Rubagotti, Antonio Estrada, Fernando Castaños, Antonella Ferrara, Leonid M. Fridman
- IEEE Trans. Automat. Contr.
- 2011

We consider the problem of designing an integral sliding mode controller to reduce the disturbance terms that act on nonlinear systems with state-dependent drift and input matrix. The general case of both, matched and unmatched disturbances affecting the system is addressed. It is proved that the definition of a suitable sliding manifold and the generation… (More)

- Igor Boiko, Leonid M. Fridman
- IEEE Trans. Automat. Contr.
- 2005

An analysis of two most popular continuous sliding-mode algorithms: The power-fractional sliding-mode algorithm and a second-order sliding-mode algorithm known as the super-twisting is carried out in the frequency domain with the use of the describing function method. It is shown that in the presence of an actuator, the transient process converges to a… (More)

- Marco Tulio Angulo, Jaime A. Moreno, Leonid M. Fridman
- Automatica
- 2013

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)

- Francisco Javier Bejarano, Leonid M. Fridman, Alexander S. Poznyak
- Int. J. Control
- 2007

The problem of the realization of integral sliding mode controllers based only on output information is discussed. The implementation of an output integral sliding mode controller ensures insensitivity of the state trajectory with respect to the matched uncertainties from the initial time moment. In the case when the number of inputs is more than or equal… (More)

- Igor Boiko, Leonid M. Fridman, M. I. Castellanos
- IEEE Trans. Automat. Contr.
- 2004

A frequency domain analysis of the second order sliding mode algorithms, particularly of the twisting algorithm is carried out with the use of the describing function and the locus of a perturbed relay system approach. It is shown that in the presence of an actuator, the transient process converges to a periodic motion. Parameters of this periodic motion… (More)

- Francisco Javier Bejarano, Leonid M. Fridman
- Int. J. Control
- 2010

Abstract: A global observer is designed for strongly detectable systems with unbounded unknown inputs. The design of the observer is based on three steps. First, the system is extended taking the unknown inputs (and possibly some of their derivatives) as a new state; then, using a global high-order sliding mode differentiator, a new output of the system is… (More)

- Leonid M. Fridman, Jorge Davila, Arie Levant
- CDC
- 2007