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Avtomat. i Telemekh., 2005, Issue 4, Pages 3–59 (Mi at1352)  

This article is cited in 36 scientific papers (total in 36 papers)


Partial stability and control: The state-of-the-art and development prospects

V. I. Vorotnikovab

a Ural State Technical University
b Nizhny Tagil Technological Institute (branch) of Ural State Technical University

Abstract: Problems in bordering fields associated with partial stability and stabilization of nonlinear dynamic systems, including partial stability and stabilization by part of coordinates of the phase vector, are reviewed. They are classified, and their relation with other stability and stabilization problems, including recent ones, are considered. Main development trends in theory and research methods are surveyed and certain results and applications are described. The partial control notion in border disciplines is examined. A long list of references is given.

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English version:
Automation and Remote Control, 2005, 66:4, 511–561

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Presented by the member of Editorial Board: Л. Б. Рапопорт

Received: 27.11.2003

Citation: V. I. Vorotnikov, “Partial stability and control: The state-of-the-art and development prospects”, Avtomat. i Telemekh., 2005, no. 4, 3–59; Autom. Remote Control, 66:4 (2005), 511–561

Citation in format AMSBIB
\by V.~I.~Vorotnikov
\paper Partial stability and control: The state-of-the-art and development prospects
\jour Avtomat. i Telemekh.
\yr 2005
\issue 4
\pages 3--59
\jour Autom. Remote Control
\yr 2005
\vol 66
\issue 4
\pages 511--561

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    This publication is cited in the following articles:
    1. Jigui Jian, Qi Guo, “Partial stability of large-scale discrete systems with unstable isolated subsystems”, Dynamics of Continuous Discrete and Impulsive Systems-Series B-Applications & Algorithms, 13:1 Suppl. S Supplement: Part 1 Suppl. S (2006), 39–42  mathscinet  isi
    2. Jian J., Shen Ya., Liao X., “Equivalent conditions of partial stability for linear time-varying discrete systems”, Dynamics of Continuous Discrete and Impulsive Systems-Series B-Applications & Algorithms, 13:2 Suppl. S Supplement: Part 2 Suppl. S (2006), 578–580  isi
    3. Jian J., Yu H., “Research on relations for partial stability of linear time-varying discrete systems and its perturbed systems”, Dyn Contin Discrete Impuls Syst Ser A Math Anal, 13:1 Suppl. S Supplement: Part 1 Suppl. S (2006), 295–297  isi
    4. Hadjiski M.B., Sgurev V.S., Boishina V.G., “Intelligent agents based non-square plants control”, 2006 3rd International IEEE Conference Intelligent Systems, 2006, 406–411  isi
    5. Stipanovic D.M., Hokayem P.F., Spong M.W., Siljak D.D., “Cooperative avoidance control for multiagent systems”, Journal of Dynamic Systems Measurement and Control-Transactions of the Asme, 129:5 (2007), 699–707  crossref  mathscinet  isi  scopus
    6. Alekseyeva C.A., Vorotnikov V.I., Feofanova V.A., “Problems of the partial stability and detectability of dynamical systems”, J Appl Math Mech, 71:6 (2007), 869–879  crossref  mathscinet  adsnasa  isi  elib  scopus
    7. Valicka Ch.G., Bieniawski S.R., Stipanovic D.M., Vian J., “Cooperative Avoidance Control for UAVs”, 2008 10th International Conference on Control Automation Robotics & Vision: ICARV 2008, 2008, 1462–1468  crossref  isi  scopus
    8. V. I. Vorotnikov, Yu. G. Martyshenko, “On partial detectability of the nonlinear dynamic systems”, Autom. Remote Control, 70:1 (2009), 20–32  mathnet  crossref  mathscinet  zmath  isi
    9. Hu W., Wang J., Li X., “An approach of partial control design for system control and synchronization”, Chaos Solitons & Fractals, 39:3 (2009), 1410–1417  crossref  mathscinet  zmath  adsnasa  isi  scopus
    10. A. V. Schennikov, “Printsip vklyucheniya i ustoichivopodobnye svoistva «chastichnogo» polozheniya ravnovesiya dinamicheskoi sistemy”, Vestn. S.-Peterburg. un-ta. Ser. 10. Prikl. matem. Inform. Prots. upr., 2011, no. 4, 119–132  mathnet
    11. Kozlov M.V., Schennikov V.N., “Odin podkhod k issledovaniyu ustoichivosti reshenii singulyarno vozmuschennykh sistem differentsialnykh uravnenii”, Izvestiya vysshikh uchebnykh zavedenii. Povolzhskii region. Fiziko-matematicheskie nauki, 2011, no. 2, 49–57  elib
    12. Binazadeh T., Yazdanpanah M.J., “Partial stabilization of uncertain nonlinear systems”, Isa Transactions, 51:2 (2012), 298–303  crossref  isi  elib  scopus
    13. Binazadeh T., Yazdanpanah M.-J., “Robust partial control design for non-linear control systems: a guidance application”, Proceedings of the Institution of Mechanical Engineers Part I-Journal of Systems and Control Engineering, 226:I2 (2012), 233–242  crossref  isi  scopus
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    18. Jammazi Ch., “A Discussion on the Holder and Robust Finite-Time Partial Stabilizability of Brockett's Integrator”, ESAIM-Control OPtim. Calc. Var., 18:2 (2012), 360–382  crossref  mathscinet  zmath  isi  elib  scopus
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    20. Ibeas A., de la Sen M., Alonso-Quesada S., Nistal R., “Partial Stability of Controlled Seir Epidemic Models”, 2013 European Control Conference (Ecc), IEEE, 2013, 3101–3106  isi
    21. V. I. Vorotnikov, Yu. G. Martyshenko, “Stability in Part of the Variables of “Partial” Equilibria of Systems with Aftereffect”, Math. Notes, 96:4 (2014), 477–483  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    22. Goebel R., “Robustness of Stability Through Necessary and Sufficient Lyapunov-Like Conditions For Systems With a Continuum of Equilibria”, Syst. Control Lett., 65 (2014), 81–88  crossref  mathscinet  zmath  isi  elib  scopus
    23. Vazquez C. Aranovskiy S. Freidovich L., “Sliding Mode Control of a Forestry-Standard Mobile Hydraulic System”, 2014 13Th International Workshop on Variable Structure Systems (Vss), IEEE International Workshop on Variable Structure Systems, IEEE, 2014  isi
    24. Kellett Ch.M., “Classical Converse Theorems in Lyapunov'S Second Method”, Discrete Contin. Dyn. Syst.-Ser. B, 20:8 (2015), 2333–2360  crossref  mathscinet  zmath  isi  elib  scopus
    25. K. S. Lapin, “Partial Total Boundedness of Solutions to Systems of Differential Equations with Partly Controlled Initial Conditions”, Math. Notes, 99:2 (2016), 253–260  mathnet  crossref  crossref  mathscinet  isi  elib
    26. Golestani M., Mohammadzaman I., Yazdanpanah M.J., “Robust Finite-Time Stabilization of Uncertain Nonlinear Systems Based on Partial Stability”, Nonlinear Dyn., 85:1 (2016), 87–96  crossref  mathscinet  zmath  isi  elib  scopus
    27. Razmjooei H., Shafiei M.H., “a New Approach To Design a Robust Partial Control Law For the Missile Guidance Problem”, Control Eng. Appl. Inform., 18:1 (2016), 3–10  isi  elib
    28. Kankanamalage H.G., Wang Yu., “Lyapunov Descriptions of Robust Output Stability For Systems With Delays”, 2016 IEEE 55Th Conference on Decision and Control (Cdc), IEEE Conference on Decision and Control, IEEE, 2016, 6416–6421  isi
    29. Aleksandrov A., Aleksandrova E., Zhabko A., Chen Ya., “Partial Stability Analysis of Some Classes of Nonlinear Systems”, Acta Math. Sci., 37:2 (2017), 329–341  crossref  mathscinet  zmath  isi  scopus
    30. Capeans R., Sabuco J., Sanjuan M.A.F., Yorke J.A., “Partially Controlling Transient Chaos in the Lorenz Equations”, Philos. Trans. R. Soc. A-Math. Phys. Eng. Sci., 375:2088 (2017), 20160211  crossref  mathscinet  isi  scopus
    31. Kankanamalage H.G., Lin Yu., Wang Yu., “On Lyapunov-Krasovskii Characterizations of Input-to-Output Stability”, IFAC PAPERSONLINE, 50:1 (2017), 14362–14367  crossref  isi  scopus
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