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The design of digital stabilizing regulators for continuous systems based on the Lyapunov function approach

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Abstract

New results regarding asymptotic stability of continuous systems with piecewise constant control are derived. The results are expressed in terms of the Lyapunov-Razumikhin functions, taking into account the specifics of the selected type of control. Certain illustrative examples are provided.

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References

  1. Naghshtabrizi, P. and Hespanha, J.P., Stability of Networks Control Systems with Variable Sampling and Delay, Proc. 44th Ann. Allerton Conf. on Communications, Control and Computing, Monticello, 2006.

  2. Polyakov, K.Yu., Digital Stabilization of Continuous Plants with Multiple Delays, Izv. Ross. Akad. Nauk, Teor. Sist. Upravlen., 2006, no. 1, pp. 26–33.

  3. Rozenvasser, E.N., Lineinaya teoriya tsifrovogo upravleniya v nepreryvnom vremeni (The Linear Theory of Digital Control in Continuous Time), Moscow: Nauka, 1994.

    Google Scholar 

  4. Kuo, B.C., Digital Control Systems, New York: Holt, Rinehart and Winston, 1980. Translated under the title Teoriya i proektirovanie tsifrovykh sistem upravleniya, Moscow: Mashinostroenie, 1986.

    Google Scholar 

  5. Monako, S. and Normand-Cyrot, D., Issues on Nonlinear Digital Control, Eur. J. Control, 2001, no. 1, pp. 160–177.

  6. Kozlova, O.R. and Kozlov, R.I., Investigation of Stability of Nonlinear Continuous-Discrete Models of Economic Dynamics Using Vector Lyapunov Function. I, II, Izv. Ross. Akad.Nauk, Teor. Sist. Upravlen., 2009, no. 2, pp. 104–113; no. 3, pp. 41–50.

  7. Polyakov, K.Yu. and Rybinskii, V.O., Optimal Choice of Sampling Period in a Digital Ship Control System, Tr. VII Konf. Molodykh Uchenykh “Navigats. Upravlen. Dvizhen. ” (Proc. VII Young Scientist Conf. “Navigation and Motion Control”), St. Petersburg, 2006, pp. 106–113.

  8. Akhmet, M. and Arugaslan, D., Lyapunov-Razumikhin Method for Differential Equations with Piecewise Constant Argument, Discr. Cont. Dynam. Syst., 2009, vol. 25, no. 2, pp. 457–466.

    Article  MathSciNet  MATH  Google Scholar 

  9. Wu, Y.-Y. and Wu, Y.-Q., Stability Analysis for Recurrent Neural Networks with Time-varying Delay, Int. J. Automat. Comput., 2009, vol. 6, no. 3, pp. 223–227.

    Article  Google Scholar 

  10. Karafyllis, I. and Kravaris, C., Global Stability Results for System under Sampled-Data Control, Proc. Eur. Control Conf., Kos, Greece, 2007, pp. 5761–5768.

  11. Artstein, Z., Topological Dynamics of Ordinary Differential Equations, J. Differ. Equat., 1977, vol. 23, pp. 216–223.

    Article  MathSciNet  MATH  Google Scholar 

  12. Hale, J.K., Functional Differential Equations, New York: Springer-Verlag, 1971. Translated under the title Teoriya funktsional’no-differentsial’nykh uravnenii, Moscow: Mir, 1984.

    Book  MATH  Google Scholar 

  13. Sedova, N.O., On the Principle of Reduction for the Nonlinear Delay Systems, Autom. Remote Control, 2011, vol. 72, no. 9, pp. 1864–1875.

    Article  MathSciNet  MATH  Google Scholar 

  14. Sedova, N.O., Degenerate Functions in the Analysis of Asymptotic Stability of Solutions of Functional Differential Equations, Math. Notes, 2005, vol. 78, nos. 3–4, pp. 427–431.

    Article  MathSciNet  MATH  Google Scholar 

  15. Razumikhin, B.S., Ustoichivost’ ereditarnykh sistem (Stability of Hereditary Systems), Moscow: Nauka, 1988.

    Google Scholar 

  16. Sontag, E.D., Nonlinear Analysis, Differential Equations and Control, in NATO Sci. Ser. C, Math. Phys. Sci., Dordrecht: Kluwer, 1999, vol. 528, pp. 551–598.

    Google Scholar 

  17. Clarke, F.H., Ledyaev, Yu.S., Sontag, E.D., and Subbotin, A.I., Asymptotic Controllability Implies Feedback Stabilization, IEEE Trans. Autom. Control, 1992, vol. 42, pp. 1394–1407.

    Article  MathSciNet  Google Scholar 

  18. Sedova, N.O., The Global Asymptotic Stability and Stabilization in Nonlinear Cascade Systems with Delay, Russ. Math. (Iz. VUZ), 2008, vol. 52, no. 11, pp. 60–69.

    MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Ulyanovsk State University, Ulyanovsk, Russia

    N. O. Sedova

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  1. N. O. Sedova
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Original Russian Text © N.O. Sedova, 2011, published in Problemy Upravleniya, 2011, No. 6, pp. 7–13.

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Sedova, N.O. The design of digital stabilizing regulators for continuous systems based on the Lyapunov function approach. Autom Remote Control 73, 1572–1580 (2012). https://doi.org/10.1134/S000511791209010X

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  • DOI: https://doi.org/10.1134/S000511791209010X

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