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- Arie Levant
- 2003

Being a motion on a discontinuity set of a dynamic system, sliding mode is used to keep accurately a given constraint and features theoretically-infinite-frequency switching. Standard sliding modes provide for finite-time convergence, precise keeping of the constraint and robustness with respect to internal and external disturbances. Yet the relative degree… (More)

- Arie Levant
- 2001

One of the most important control problems is control under heavy uncertainty conditions. While there are a number of sophisticated methods like adaptation based on identi cation and observation, or absolute stability methods, the most obvious way to withstand the uncertainty is to keep some constraints by "brutal force". Indeed any strictly kept equality… (More)

- Arie Levant
- IEEE Trans. Automat. Contr.
- 2005

A universal finite-time-convergent controller is developed capable to control the output of any uncertain single-input-single-output system with a known permanent relative degree . The tracking error is steered to zero by means of a control dependent only on _ . . . and continuous everywhere except the set = _ = = = 0. A robust output-feedback controller… (More)

- Arie Levant
- Automatica
- 2005

It is shown that a general uncertain single-input–single-output regulation problem is solvable only by means of discontinuous control laws, giving rise to the so-called high-order sliding modes. The homogeneity properties of the corresponding controllers yield a number of practically important features. In particular, finite-time convergence is proved, and… (More)

- 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.

- Arie Levant
- Automatica
- 2007

Second-order sliding modes are used to keep exactly a constraint of the second relative degree or just to avoid chattering, i.e. in the cases when the standard (first order) sliding mode implementation might be involved or impossible. Design of a number of new 2-sliding controllers is demonstrated by means of the proposed homogeneity-based approach. A… (More)

- Arie Levant
- 2001

An universal controller is constructed, formulated in input-output terms only, which causes the output of any uncertain smooth SISO minimum-phase dynamic system with known relative degree to vanish in finite time. That allows exact tracking of arbitrary real-time smooth signals. Only one parameter is to be adjusted. The approach being based on higher-order… (More)

- Arie Levant
- IEEE Trans. Automat. Contr.
- 2001

- Arie Levant, Miki Livne
- IEEE Trans. Automat. Contr.
- 2012

Arbitrary-order homogeneous differentiators based on highorder sliding modes are generalized to ensure exact robust kth-order differentiation of signals with a given functional bound of the th derivative. The asymptotic accuracies in the presence of noises and discrete sampling are estimated. The results are applicable for the global observation of system… (More)

- Arie Levant
- 2000

Control of high-performance low-cost unmanned air vehicles involves the problems of incomplete measurements, external disturbances and modeling uncertainties. Sliding mode control combines high precision with robustness to the aforementioned factors. The idea behind this approach is the choice of a particular constraint which, when maintained, will provide… (More)