A. P. Molchanov, E. S. Pyatnitskiǐ, “Lyapunov functions detemining the necessary and sufficient conditions for absolute stability of nonlinear nostationary control systems. III”, Avtomat. i Telemekh., 1986, no. 5, 38–49; Autom. Remote Control, 47:5 (1986), 620

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Avtomatika i Telemekhanika, 1986, Issue 5, Pages 38–49 (Mi at6230)

This article is cited in 13 scientific papers (total in 13 papers)

Deterministic Systems

Lyapunov functions detemining the necessary and sufficient conditions for absolute stability of nonlinear nostationary control systems. III

A. P. Molchanov, E. S. Pyatnitskiĭ

Moscow

Full-text PDF (1798 kB) Citations (13)

Abstract: For nonlinear control systems incorporating several nonlinear elements that satisfy sector-like constraints the necessary and sufficient stability conditions are obtained in terms of solvability of a system of matrix equations. In a similar form, the necessary and sufficient conditions are found for asymptotical stability of linear stationary systems, and differential inclusions of a special form.

Received: 12.06.1985

Bibliographic databases:

Document Type: Article

UDC: 62-501.52

Language: Russian

Citation: A. P. Molchanov, E. S. Pyatnitskiǐ, “Lyapunov functions detemining the necessary and sufficient conditions for absolute stability of nonlinear nostationary control systems. III”, Avtomat. i Telemekh., 1986, no. 5, 38–49; Autom. Remote Control, 47:5 (1986), 620–630

Citation in format AMSBIB

\Bibitem{MolPya86}

\by A.~P.~Molchanov, E.~S.~Pyatnitski{\v\i}

\paper Lyapunov functions detemining the necessary and sufficient conditions for absolute stability of nonlinear nostationary control systems.~III

\jour Avtomat. i Telemekh.

\yr 1986

\issue 5

\pages 38--49

\mathnet{http://mi.mathnet.ru/at6230}

\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=854335}

\zmath{https://zbmath.org/?q=an:0626.93051}

\transl

\jour Autom. Remote Control

\yr 1986

\vol 47

\issue 5

\pages 620--630

Linking options:

https://www.mathnet.ru/eng/at6230

https://www.mathnet.ru/eng/at/y1986/i5/p38

This publication is cited in the following 13 articles:

A. M. Musaeva, “Dvoistvennost invariantnykh norm v dinamicheskikh sistemakh s nepreryvnym vremenem”, Matem. zametki, 117:2 (2025), 295–304
Rinat A. Kamalov, Vladimir Yu. Protasov, “On the Length of Switching Intervals of a Stable Dynamical System”, Proc. Steklov Inst. Math., 321 (2023), 149–157
Vladimir Yu. Protasov, “Generalized Markov–Bernstein Inequalities and Stability of Dynamical Systems”, Proc. Steklov Inst. Math., 319 (2022), 237–252
Berdnikov V. Lokhin V., “Synthesis of Guaranteed Stability Regions of a Nonstationary Nonlinear System With a Fuzzy Controller”, Civ. Eng, J.-Tehran, 5:1 (2019), 107–116
Demenkov M., “Constructing Control Lyapunov Functions From Polyhedral Controllable Sets Using Frank-Wolfe Algorithm”, IFAC PAPERSONLINE, 51:32 (2018), 153–156
Guglielmi N. Laglia L. Protasov V., “Polytope Lyapunov Functions For Stable and For Stabilizable Lss”, Found. Comput. Math., 17:2 (2017), 567–623
Berdnikov V.P. Lohin V.M., “Calculation of Absolute Stability Regions For Time-Varying Electromechanical Systems”, International Conference on Information Technologies in Business and Industry 2016, Journal of Physics Conference Series, 803, ed. Martyushev N. Avramchuk V. Faerman V., IOP Publishing Ltd, 2017, UNSP 012020
Kellett Ch.M., “Classical Converse Theorems in Lyapunov'S Second Method”, Discrete Contin. Dyn. Syst.-Ser. B, 20:8 (2015), 2333–2360
Athanasopoulos N. Bitsoris G. Lazar M., “Construction of Invariant Polytopic Sets With Specified Complexity”, Int. J. Control, 87:8 (2014), 1681–1693
Athanasopoulos N. Bitsoris G. Lazar M., “Complexity-Driven Construction of Controlled Invariant Polytopic Sets”, 2013 17th International Conference on System Theory, Control and Computing (Icstcc), ed. Petre E. Brezovan M., IEEE, 2013, 29–36
V. N. Zhermolenko, “Periodic motions and criteria of absolute stability, instability, and controllability of two-dimensional bilinear systems”, Autom. Remote Control, 67:8 (2006), 1194–1214
M. R. Liberzon, “Essays on the absolute stability theory”, Autom. Remote Control, 67:10 (2006), 1610–1644
V. N. Zhermolenko, “Oscillativity of two-dimensional bilinear systems”, Autom. Remote Control, 66:9 (2005), 1384–1395

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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