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Avtomat. i Telemekh., 2006, Issue 10, Pages 86–119 (Mi at1246)  

This article is cited in 43 scientific papers (total in 43 papers)

Essays on the absolute stability theory

M. R. Liberzon

Moscow State Aviation Technological University

Abstract: A brief historical background of the development of the absolute stability theory was presented, and some of its methods and approaches, as well as the results obtained using them, were discussed. The kinds of systems under consideration are named, and applications of the methods and results of the absolute stability theory to other scientific and practical fields for solution of the engineering, mechanical, physical, and other problems were presented.

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English version:
Automation and Remote Control, 2006, 67:10, 1610–1644

Bibliographic databases:

PACS: 02.30.Yy
Presented by the member of Editorial Board: Б. Т. Поляк

Received: 25.01.2006

Citation: M. R. Liberzon, “Essays on the absolute stability theory”, Avtomat. i Telemekh., 2006, no. 10, 86–119; Autom. Remote Control, 67:10 (2006), 1610–1644

Citation in format AMSBIB
\by M.~R.~Liberzon
\paper Essays on the absolute stability theory
\jour Avtomat. i Telemekh.
\yr 2006
\issue 10
\pages 86--119
\jour Autom. Remote Control
\yr 2006
\vol 67
\issue 10
\pages 1610--1644

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    3. G. A. Leonov, “On the Aizerman problem”, Autom. Remote Control, 70:7 (2009), 1120–1131  mathnet  crossref  mathscinet  zmath  isi  elib  elib
    4. Gil' Michael, “Absolute and Input-to-State Stabilities of Nonautonomous Systems with Causal Mappings”, Dynam Systems Appl, 18:3–4 (2009), 655–666  mathscinet  zmath  isi  elib
    5. Benosman M., Lum K.-Y., “Application of absolute stability theory to robust control against loss of actuator effectiveness”, Iet Control Theory and Applications, 3:6 (2009), 772–788  crossref  mathscinet  isi  scopus
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    8. Altshuller D.A., “Delay-Integral-Quadratic Constraints and Stability Multipliers for Systems With MIMO Nonlinearities”, IEEE Trans Automat Control, 56:4 (2011), 738–747  crossref  mathscinet  zmath  isi  elib  scopus
    9. Brogliato B., Goeleven D., “Well-posedness, stability and invariance results for a class of multivalued Lur'e dynamical systems”, Nonlinear Analysis-Theory Methods & Applications, 74:1 (2011), 195–212  crossref  mathscinet  zmath  isi  scopus
    10. A. I. Barkin, “Absolute stability and harmonic balance”, Autom. Remote Control, 72:9 (2011), 1800–1807  mathnet  crossref  mathscinet  zmath  isi
    11. Jayawardhana B., Logemann H., Ryan E.P., “The Circle Criterion and Input-to-State Stability NEW PERSPECTIVES ON A CLASSICAL RESULT”, IEEE Control Systems Magazine, 31:4 (2011), 32–67  crossref  mathscinet  isi  scopus
    12. Barkin A.I., “Otsenka oblasti ustoichivosti nelineinoi sistemy putem razbieniya lineinogo bloka na podsistemy”, Informatsionnye tekhnologii i vychislitelnye sistemy, 2011, no. 1, 3–7  elib
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    14. Fainshil L. Margaliot M., “A Maximum Principle for the Stability Analysis of Positive Bilinear Control Systems with Applications to Positive Linear Switched Systems”, SIAM J. Control Optim., 50:4 (2012), 2193–2215  crossref  mathscinet  zmath  isi  elib  scopus
    15. V. V. Aleksandrov, I. O. Zueva, G. Yu. Sidorenko, “Robust stability of third-order control systems”, Moscow University Mechanics Bulletin, 69:1 (2014), 10–15  mathnet  crossref
    16. Zhao X. Gan Z., “the Absolute Stability For General Discrete Lurie Systems With Superposition of Multiple Nonlinearities”, Appl. Math. Comput., 259 (2015), 490–496  crossref  mathscinet  zmath  isi  elib  scopus
    17. Klug M., Castelan E.B., Leite V.J.S., Silva L.F.P., “Fuzzy Dynamic Output Feedback Control Through Nonlinear Takagi-Sugeno Models”, Fuzzy Sets Syst., 263 (2015), 92–111  crossref  mathscinet  zmath  isi  elib  scopus
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    19. Sarkans E., Logemann H., “Input-To-State Stability of Lur'E Systems”, Math. Control Signal Syst., 27:4 (2015), 439–465  crossref  mathscinet  zmath  isi  elib  scopus
    20. Zhang Y., Zhao Yu., Xu T., Liu X., “Pth Moment Absolute Exponential Stability of Stochastic Control System With Markovian Switching”, J. Ind. Manag. Optim., 12:2 (2016), 471–486  crossref  mathscinet  zmath  isi
    21. Adly S., Hantoute A., Khiet Le B., “Nonsmooth Lur'E Dynamical Systems in Hilbert Spaces”, Set-Valued Var. Anal., 24:1, SI (2016), 13–35  crossref  mathscinet  zmath  isi  scopus
    22. Lauret M., Lennholm M., de Baar M.R., Heemels W. P. M. H., “Pacing Control of Sawtooth and Elm Oscillations in Tokamaks”, Plasma Phys. Control. Fusion, 58:12 (2016), 124004  crossref  isi  scopus
    23. Lipkovich M. Fradkov A., “Equivalence of Mimo Circle Criterion To Existence of Quadratic Lyapunov Function”, IEEE Trans. Autom. Control, 61:7 (2016), 1895–1899  crossref  mathscinet  zmath  isi  elib  scopus
    24. Camlibel M.K., Schumacher J.M., “Linear Passive Systems and Maximal Monotone Mappings”, Math. Program., 157:2, SI (2016), 397–420  crossref  mathscinet  zmath  isi  elib  scopus
    25. Carrasco J., Turner M.C., Heath W.P., “Zames-Falb Multipliers For Absolute Stability: From O'Shea'S Contribution To Convex Searches”, Eur. J. Control, 28 (2016), 1–19  crossref  mathscinet  zmath  isi  elib  scopus
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