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Control of nonlinear and uncertain systems modal control under interval uncertainty of parameters

  • Methods of Analysis and Modeling of Nonlinear Dynamic Systems
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References

  1. S. Faedo, "Un nuovo problema di stabilita per le equazioni algebriche a coefficienti reali," Ann. Scuola Nom. Super. Piza, Sci. Fis. Mat.,7, No. 1–2, 53–63 (1953).

    Google Scholar 

  2. V. L. Kharitonov, "Asymptotic stability of equilibria of a family of systems of linear differential equations," Diff. Uravn.,14, No. 11, 2086–2088 (1978).

    Google Scholar 

  3. S. S. Chang and T. K. S. Peng, "Adaptive guaranteed cost control of systems with uncertain parameters," IEEE Trans. Autom. Contr.,AC-17, No. 4, 474–483 (1972).

    Google Scholar 

  4. I. R. Petersen and M. R. Pickering, "Riccati equations in the stabilization of uncertain systems: a comparison between the methods of Chang—Peng and Petersen—Hollot," in: Preprints of 11th IFAC World Congr., Tallin (1990), pp. 317–321.

  5. N. A. Khlebalin, "Analytical method of controller synthesis with uncertain plant parameters," in: Analytical Methods of Controller Synthesis [in Russian], Inter-Univ. Proc., Saratov. Politekh. Inst., Saratov (1981), pp. 107–123.

    Google Scholar 

  6. R. E. Moore, Interval Analysis, Prentice-Hall, Englewood Cliffs, N.J. (1966).

    Google Scholar 

  7. N. T. Kuzovkov, Aircraft Stabilization Systems [in Russian], Vysshaya Shkola, Moscow (1976).

    Google Scholar 

  8. Yu. I. Shokin, Interval Analysis [in Russian], Nauka, Novosibirsk (1981).

    Google Scholar 

  9. G. Reklaitis, A. Ravindran, and K. Ragsdell, Engineering Optimization [Russian translation], Vol. 2, Mir, Moscow (1986).

    Google Scholar 

  10. J. L. Melsa and S. K. Jones, Computer Programs for Computational Assistance in the Study of Linear Control Systems [Russian translation], Mashinostroenie, Moscow (1981).

    Google Scholar 

  11. N. A. Khlebalin, "Guaranteed solution of systems of linear interval algebraic equations," in: Distributed Information-Control Systems [in Russian], Izd. Saratov. Univ., Saratov (1988), p. 138.

    Google Scholar 

  12. S. P. Sharyi, "On some solution methods for the linear tolerance problem," Preprint No. 6, VTs SO Akad. Nauk SSSR, Krasnoyarsk (1989).

    Google Scholar 

  13. N. A. Khlebalin, "Analysis of controllability-observability and controller synthesis for stationary multidimensional continuous plants in the presence of uncertain parametric perturbations," in: Development of Methods of Analytical Synthesis of Controllers for Multidimensional Systems [in Russian] (1983), pp. 56–64.

  14. N. A. Khlebalin, "Construction of interval polynomials with a given root localization region," in: Analytical Methods of Controller Synthesis [in Russian], Inter-Univ. Proc. Saratov. Politekhn. Inst., Saratov (1982), pp. 92–98.

    Google Scholar 

  15. N. A. Khlebalin, "Synthesis of interval controllers in the modal control problem," in: Analytical Methods of Controller Synthesis [in Russian], Inter-Univ. Proc. Saratov. Politekhn. Inst., Saratov (1988), pp. 26–30.

    Google Scholar 

  16. N. A. Khlebalin, "Qualitative assessment of controllability of plants described by differential equations with uncertain coefficients," in: 6th All-Union Conf. on Qualitative Theory of Differential Equations, abstracts of papers [in Russian], Irkutsk (1986), pp. 193–195.

  17. A. V. Zakharov and Yu. I. Shokin, "Synthesis of control systems in the presence of interval uncertainty of parameters in their mathematical models," Dokl. Akad. Nauk SSSR,299, No. 2, 292–295 (1988).

    Google Scholar 

  18. E. M. Smagina and I. V. Dugarova, "Synthesis of a modal controller for a system with uncertain parameters," Tomsk (1987). Unpublished manuscript, VINITI No. 789-V87.

  19. R. T. Sirazetdinov, "Synthesis of the set of controls guaranteeing the desired performance of linear stationary systems with uncertain parameters," in: 11th All-Union Conf. on Control Problems, abstracts of papers [in Russian], Tashkent (1989), pp. 23–24.

  20. A. K. Samorukov, N. A. Khlebalin, and A. V. Zakharov, "Controller synthesis for stabilization of lateral motion of a helicopter towing system in the presence of uncertain parameters in the mathematical models," in: Analytical Methods of Controller Synthesis [in Russian], Inter-Univ. Proc. Saratov. Politekhn. Inst., Saratov (1982), pp. 109–122.

    Google Scholar 

  21. G. Alefeld and J. Herzberger, Introduction to Interval Computations, Academic Press, New York (1983).

    Google Scholar 

  22. G. Korn and T. Korn, Mathematical Handbook for Scientists and Engineers, McGraw-Hill, New York (1961).

    Google Scholar 

  23. V. P. Sigorskii, The Mathematical Apparatus of Engineers [in Russian], Tekhnika, Kiev (1977).

    Google Scholar 

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Translated from Upravlenie Nelineinymi Sistemami, Vsesoyuznyi Nauchno-Issledovatel'skii Institut Sistemnykh Issledovanii, Sbornik Trudov, No. 4, pp. 50–59, 1991.

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Khlebalin, N.A. Control of nonlinear and uncertain systems modal control under interval uncertainty of parameters. Comput Math Model 5, 44–51 (1994). https://doi.org/10.1007/BF01128578

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