Home Page by Levant

Levant, Arie ( formerly Levantovsky, Lev )


Applied Mathematics Dept.,
School of Mathematical Sciences,
Tel-Aviv University,
Tel-Aviv 69978

E-mail: levant@post.tau.ac.il
Tel.: +972-3-6408812 (office), Fax: +972-3-6407543


Spring 2017. Reception Hours: Tuesday, 14:10 - 15:00, Room 320, Schreiber building


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

1983-1987 Postgraduate studies on speciality "Control theory", Institute for System Studies of the USSR Academy of Science, Moscow.

1980 B.Sc. and M.Sc. Moscow State University, Faculty of Mechanics and Mathematics, majored in Differential Equation Theory.

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

Publications: More than 100 scientific publications

Awards: 1988 VLKSM Prize (Union of the Soviet Youth) for solving Control Problems of Dynamic Systems (with K.V. Malkov, I.G. Mamedov, A.L. Nersisyan, S.V. Nikitin, V.I. Sizikov)

Research Interests:

Nonlinear Control Theory, Variable Structure Systems, Higher-Order Sliding Modes, High-Precision Tracking, Real-Time Control, Image Processing, Computer Vision.

Main scientific result:

Establishment of a new branch of the Sliding-Mode Control Theory - High-Order Sliding Modes

My papers on Google Scholar Kovalskie

Some papers in the PDF format:

Sliding order and sliding accuracy in sliding mode control (International Journal of Control, 58(6), 1993, 1247-1263)

High order sliding modes in control systems (with Emelyanov and Korovin, Computational Mathematics and Modeling, 7(3), 294--318, 1996)

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

Aircraft Pitch Control via Second Order Sliding Technique (with Pridor A., Gitizadeh R., Yaesh I., Ben-Asher J. Z., AIAA Journal of Guidance, Control and Dynamics, 23(4), 2000, 586-594 )

Proofs for the paper IEEE Transactions on Automatic Control, 46(9), 2001, pp. 1447 - 1451 - see the paper in Int. J. of Control, 76 (9/10), 924-941, 2003

Universal SISO sliding-mode controllers with finite-time convergence, IEEE Transactions on Automatic Control, 46(9), 2001, pp. 1447 - 1451

Higher order sliding modes.- with Fridman L.- in W. Perruquetti, J. P. Barbot, eds. "Sliding Mode Control in Engineering", Marcel Dekker, Inc., 53-101, 2002

Higher-order sliding modes, differentiation and output-feedback control, Int. J. of Control, 76 (9/10), 924-941, Special issue on Sliding-Mode Control. , 2003

Transient adjustment of high-order sliding modes (with L. Alelishvili) - Proc. of the 7th Scientific Workshop “Variable Structure Systems VSS'2004”, Vilanova, Spain, September 6-8, 2004

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

Quasi-Continuous High-Order Sliding-Mode Controllers , IEEE Transactions on Automatic Control, 50(11), 1812-1816, 2005

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

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

Finite Differences in Homogeneous Discontinuous Control, IEEE Transactions on Automatic Control, 52(7), 1208 - 1217, 2007

Integral High-Order Sliding Modes (with L. Alelishvili), IEEE Transactions on Automatic Control, 52(7), 1278 - 1282, 2007
Proofs for High-Order Integral Sliding Modes - see here and here

Generalized homogeneous quasi-continuous controllers (with Y.Pavlov), Int.Journal of Robust and Nonlinear Control, 18(4-5), 385 - 398, 2008 - Special Issue: Advances in Higher Order Sliding Mode Control

Keynote "Homogeneous High-Order Sliding Modes", 17th IFAC World Congress, Seoul, July 6-11, 2008

Adjustment of High-Order Sliding-Modes (with A. Michael), Int.Journal of Robust and Nonlinear Control, 19(15), 1657 - 1672, 2009

Homogeneous Sliding Modes in the Presence of Fast Actuators (with L. Fridman), IEEE Transactions on Automatic Control, 55(3), 810 - 814, 2010

Full version of the paper "Accuracy of Homogeneous Sliding Modes in the Presence of Fast Actuators" (with proofs)

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

Finite-time stability and high relative degrees in sliding-mode control. Plenary Lecture at the 11th International Workshop VSS'2010, Mexico-City, Mexico, June 26, 2010, published in Lecture Notes in Control and Information Sciences, 412, 59-92, 2012

Exact differentiation of signals with unbounded higher derivatives (with M. Livne). IEEE Transactions on Automatic Control, 57(4), 1076-1080, 2012

Practical Relative Degree Approach in Sliding-Mode Control. Plenary Lecture at the 12th Scientific Workshop VSS'11, Mumbay (India), January 12-14, 2012, published in Lecture Notes in Control and Information Sciences, 440, 97-115, 2013

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

Globally Convergent Fast Exact Differentiator with Variable Gains. In Proc. European Control Conference, June 24-27, Strasbourg, 2014

Proper discretization of homogeneous differentiators (with M. Livne), Automatica, 50(8), pp. 2007-2014, 2014

Uncertain disturbances' attenuation by homogeneous MIMO sliding mode control and its discretization (with M. Livne), IET Control Theory & Applications, 9(4), 515-525, 2015

Barbot,Levant,Livne,Luntz-Discrete Sliding-Mode-Based Differentiators,VSS2016, June 1-4, 2016, Nanjing, China

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

A. Levant, M. Livne - Weighted homogeneity and robustness of sliding mode control, Automatica, 72(10),186-193,2016

Lecture "Black-Box Control in Theory and Applications" at RMIT University, Melbourne, August 19,2016

A.Levant, M.Livne, D.Lunz-On Discretization of High Order Sliding Modes, in Barbot,Fridman,Plestan (eds) "Recent Trends in Sliding Mode Control", 177-202,IET,2016

A.Levant, D.Efimov, A.Polyakov, W.Perruquetti-Stability and Robustness of Homogeneous Differential Inclusions,CDC 2016, Las-Vegas, December 12-15, 2016

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.

Ring Tones