**Levant, Arie ( formerly Levantovsky, Lev )**

Professor of the Applied Mathematics Dept.

School of Mathematical Sciences,

Tel-Aviv University,

Ramat-Aviv.

Tel-Aviv 69978

Israel

E-mail: levant@tauex.tau.ac.il

Tel.: +972-3-6408812 (office), Fax: +972-3-6407543

"Real-time" differentiation of the noisy signal *f = f*_{0}* +h, *

representing the "unknown" basic signal *f*_{0}(*t*) = sin(0.5 *t*) + 0.5 cos(*t*)

corrupted by the noise

*h = *10^{7} cos(10^{4} *t*)
- 2 10^{7} sin(1.7 10^{5} *t*) + 5 10^{7}
cos(1.33 10^{5} *t*)

and sampled with the time period 10^{-5}.

Filtering differentiator
of the order 3 and the filtering order 7 is applied

**Teaching**
**My papers on Google Scholar**

Fall 2020. Reception Hours: Tuesday, 14:00 - 15:00, on ZOOM. In better times: Room 123a, Schreiber building

**Education:**

1987 **Ph.D.** Thesis "Higher-order sliding modes and their application in control of uncertain
processes". *Adviser*: Prof S.V. Emelyanov. *Opponent *(*secondary adviser*): Prof M.A. Krasnoselsky.

1983-1987 **Postgraduate studies** in mathematical control theory, Institute for System Studies of the USSR Academy of Sciences,
Moscow.

1980 **B.Sc. **and** M.Sc.** from the** ** Moscow State University, Faculty of Mechanics
and Mathematics, majored in the Theory of Differential Equations.

1980 **M.Sc.** Thesis "Singularities of Stability Region Boundary."
*Scientific Adviser*: Prof V.I.
Arnold.

**Research Interests:**

Nonlinear Control Theory, Sliding Mode Control, Homogeneous Discontinuous Control, Nonlinear Finite-Time-Exact Tracking and Observation, Robust Exact High-Order Differentiation.

**Main scientific results:**

Establishment of new branches of the Sliding-Mode Control (SMC) Theory - High-Order SMC and Homogeneous SMC; Real-Time Robust Exact Differentiation

Some papers in the PDF format:

**Introduction of High-Order SMs:**

A.Levant-Robust exact differentiation via sliding
mode technique, *Automatica*, 34(3), 379-384, 1998

**Introduction of homogeneous
SMC:**

A.Levant-Homogeneity
approach to high-order sliding mode design. - *Automatica*, 41(5),
823-830, 2005

A.Levant-Homogeneous quasi-continuous
sliding-mode control. *Lecture Notes in Control and
Information Sciences*, 334, 143--168, "Advances
in Variable Structure and Sliding Mode Control", 2006

A.Levant-Construction principles
of 2-sliding mode design. *Automatica*, 43(4), 576-586, 2007

A.Levant,L.Alelishvili-Integral
High-Order Sliding Modes, IEEE Transactions on Automatic Control, 52(7), 1278 - 1282, 2007

Proofs for High-Order Integral Sliding Modes - see here and here

**Artificial
increase of the output relative degree:**

A.Levant-Chattering Analysis, IEEE Transactions on Automatic Control, 55(6), 1380 - 1389, 2010

**Introduction of Practical
Relative Degree:**

**Feasibility of fixed-time convergence:**

A.Levant-On Fixed and Finite Time Stability in Sliding Mode Control. Corrected version. In_Proc._of_the 52th IEEE Conference on Decision and Control, CDC 2013, Florence, Italy, December 10-13, 2013

**Arbitrary convergence-time function realization, including
acceleration of MIMO finite-time convergence up to fixed-time convergence**

**Discretization of homogeneous SMC:**

S.Ding, A.Levant, S.Li - Simple homogeneous sliding-mode controller, Automatica, 67(5),22-32,2016

**General
weighted homogeneity of differerntial inclusions:**

**Asymptotic
optimality of SM-based differentiators:**

A.Levant, M.Livne, X.Yu-Sliding-Mode-Based Differentiation and Its Application, 20th IFAC World Congress, Toulouse, July 9-14, France, 2017. A typo has been corrected in the simulation section.

**Universal
homogeneous control templates:**

A.Levant-Non-Lyapunov SISO homogeneous control design, IEEE CDC2017

**Fast-convergent
SM-based differentiators with variable gains:**

A.Levant-Filtering Differentiators and Observers, VSS, Graz, Austria, July 9-11, 2018

**Filtering
unbounded noises in differentiation (still exact without noises!):**

A.Levant,X.Yu-Sliding Mode Based Differentiation and Filtering, IEEE TAC, 63(9), 3061-3067, 2018

A.Levant-Homogeneous filtering and differentiation based on sliding modes, IEEE CDC'2019

Presentation of Filtering Differentiators (December, 2019)

**Discretization of differentiators, event-triggered sampling:**

**SMC for students: survey-tutorial,
2019**

Lecture "Homogeneous Control and Observation of Uncertain SISO Systems", Dalian Maritime University, China, July 27, 2020, Mexico, January 13, 2021 ZOOM recording of July 27, 2020

A.Hanan, A.Jbara,A.Levant-Homogeneous sliding modes in noisy environments, in "Emerging Trends in Sliding Mode Control Theory and Application", Springer, 2021