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Some Approaches to Stabilizing Switched Linear Systems with Operation Modes of Different Dynamic Orders

  • Control Theory
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Abstract

We study the problem of stabilizing multiple-input switched linear systems that may have operation modes of different dynamic orders. To solve this problem, we propose two approaches to constructing a. stabilizing controller based on the dynamic-order extension method and on solving a. system of linear matrix inequalities.

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References

  1. Fursov, A.S., Emel’yanov, S.V., Kapalin, I.V., and Sagadinova, E.S., Stabilization of multiple-input switched linear systems with operation modes of different dynamical orders, Differ. Equations, 2018. vol. 54, no. 11, pp. 1517–1523.

    Article  MathSciNet  Google Scholar 

  2. Fursov, A.S., Odnovremennaya stabilizatsiya: teoriya postroeniya universal’nogo regulyatora dlya se-meistva dinamicheskikh ob’ektov (Simultaneous Stabilization: Theory of Constructing a. Universal Controller for a. Family of Dynamic Objects), Moscow: Argamak-Media, 2016.

    Google Scholar 

  3. Balandin, D.V. and Kogan, M.M., Sintez zakonov upravleniya na osnove lineinykh matrichnykh nera-venstv (Synthesis of Control Rules Based on Linear Matrix Inequalities), Moscow: Fizmatlit, 2007.

    Google Scholar 

  4. Barsegyan, V.R., Upravlenie sostavnykh dinamicheskikh sistem i. sistem s. mnogotochechnymi prome-zhutochnymi usloviyami (Control of Compound Dynamical Systems and a. System with Multiple-Point Intermediate Conditions), Moscow: Nauka, 2016.

    Google Scholar 

  5. Kudryavtsev, L.D., Kurs matematicheskogo analiza. T. 1 (Course of Mathematical Analysis. Vol. 1), Moscow: Vyssh. Shkola, 1981.

    MATH  Google Scholar 

  6. Fursov, A.S. and Khusainov, E.F., On the stabilization of switchable linear systems, Differ. Equations. 2015, vol. 51, no. 11, pp. 1518–1528.

    Article  MathSciNet  Google Scholar 

  7. Sun, Z. and Ge, S.S., Stability Theory of Switched Dynamical Systems, London: Spinger, 2011.

    Book  Google Scholar 

  8. Mahmoud, M.S., Switched Time-Delay Systems. Stability and Control, New York-Dordrecht-Heidelberg-London: Springer-Verlag, 2010.

    Book  Google Scholar 

  9. Johansson, M., Piecewise Linear Control System, Berlin-Heidelberg: Springer-Verlag, 2003.

    Book  Google Scholar 

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Funding

This work was supported by the Russian Foundation for Basic Research, projects nos. 18-07-01283, 18-07-01105, 17-07-00899, 16-07-00654.

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Authors and Affiliations

  1. Department of Mathematics, School of Science, Hangzhou Dianzi University, Hangzhou, China

    A. S. Fursov

  2. Lomonosov Moscow State University, Moscow, 119991, Russia

    A. S. Fursov

  3. Trapeznikov Institute of Control Sciences, Russian Academy of Sciences, Moscow, 117997, Russia

    A. S. Fursov

  4. Bauman Moscow State Technical University, Moscow, 105005, Russia

    A. S. Fursov

  5. Kharkevich Institute for Information Transmission Problems, Russian Academy of Sciences, Moscow, 127051, Russia

    A. S. Fursov

  6. National University of Science and Technology “MISiS“, Moscow, 11904-9, Russia

    I. V. Kapalin

Authors
  1. A. S. Fursov
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  2. I. V. Kapalin
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Corresponding authors

Correspondence to A. S. Fursov or I. V. Kapalin.

Additional information

Russian Text © The Author(s), 2019, published in Differentsial’nye Uravneniya, 2019, Vol. 55, No. 12, pp. 1693–1700.

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Fursov, A.S., Kapalin, I.V. Some Approaches to Stabilizing Switched Linear Systems with Operation Modes of Different Dynamic Orders. Diff Equat 55, 1641–1648 (2019). https://doi.org/10.1134/S0012266119120103

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  • DOI: https://doi.org/10.1134/S0012266119120103

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