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Machine deduction of theorems on dynamic properties with vector functions of Lyapunov

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Literature Cited

  1. V. M. Matrosov, “The comparison method in system dynamics,” Differents. Uravn., No. 9 (1974); No. 3 (1975).

  2. V. M. Matrosov and S. N. Vasil'ev, “A comparison principle for the deduction of theorems in the mathematical theory of systems,” in: Proceedings of the Fourth International United Conference on Artificial Intelligence [in Russian], VINITI, Moscow (1975).

    Google Scholar 

  3. S. N. Vasil'ev and V. M. Matrosov, “A comparison principle for theorem deduction, I, II,” Izv. Akad. Nauk SSSR, Tekh. Kibern., Nos. 2, 4 (1978).

  4. V. M. Matrosov and S. N. Vasil'ev, “Deduction of comparison theorems in the mathematical theory of systems,” in: Fourth Republic Conference of Mathematicians of Belorussian. Reports [in Russian], Part 1, Minsk (1975).

  5. V. M. Matrosov, L. Yu. Anapol'skii, and S. N. Vasil'ev, “Algorithms for comparison theorems in systems dynamics,” in: All-Union Conference on Qualitative Theory of Differential Equations. Reports and Program [in Russian], Ryazan' (1976).

  6. V. M. Matrosov and S. N. Vasil'ev, Seventh All-Union Seminar on Control Problems. Reports [in Russian], Akad. Nauk SSSR, Akad. Nauk BSSR, Minsk (1977).

    Google Scholar 

  7. V. M. Matrosov and S. N. Vasil'ev, “Comparison method in control theory in Banach space,” Preprint of Intern. Conf. “Equa-Diff 78,” Florence University (1978).

  8. A. M. Danilov, L. Z. Dul'kin, A. S. Zemlyakov, V. M. Matrosov, and V. A. Strezhnev, “The dynamics and control ofextra-atmospheric astronomical observatories,” in: Proceedings of the Sixth International Symposium of the IFAC on Automatic Control in Space [in Russian], Vol. 1, Nauka, Moscow (1976).

    Google Scholar 

  9. L. Yu. Anapol'skii, V. D. Irtegov, and V. M. Matrosov, “Methods for constructing Lyapunov functions,” in: Results of Science and Technology. General Mechanics [in Russian], Vol. 2, VINITI, Moscow (1975).

    Google Scholar 

  10. Third Chetaev Conference on Stability of Motion, Analytical Mechanics and Control of Motion. Reports [in Russian], Irkutsk (1977).

  11. V. M. Matrosov, “Comparison method in systems dynamics,” Equat. diff. et fonctions nonlineares. Actes Conf. Intern. “Equa-Diff 73,” Hermann, Paris (1973).

    Google Scholar 

  12. V. M. Matrosov and L. Yu. Anapol'skii, “Method of comparison and analysis of processes,” in: Problems of Analytical Mechanics, Theory of Stability and Control [in Russian], Nauka, Moscow (1975).

    Google Scholar 

  13. L. Yu. Anapol'skii and V. M. Matrosov, “A comparison method in systems dynamics and abstract theory of control,” Fifth Scientific Conference on Mathematics and Mechanics by Higher Learning Establishments. Papers [in Russian], Part 1, Alma-Ata (1974).

  14. S. N. Vasil'ev, “Systems, properties and quasiordering of properties,” Tr. Kaz. Aviats. Inst., No. 184 (1975).

  15. S. N. Vasil'ev and V. M. Matrosov, “A comparison principle in the mathematical theory of systems,” in: Fifth Kazakhstan Scientific Conference on Mathematics and Mechanics by Higher Learning Establishments. Papers [in Russian], Part 1, Alma-Ata (1974).

  16. S. N. Vasil'ev, “Development of the comparison principle for algorithmization of theorem deduction with analogs of Lyapunov functions and morphisms,” in: All-Union Symposium on Artificial Intelligence and Automation of Investigations in Mathematics. Papers [in Russian], Kiev (1978).

  17. K. S. Sibirskii, An Introduction to Topological Dynamics [in Russian], Akad. Nauk MSSR, Kishinev (1970).

    Google Scholar 

  18. R. C. Lyndon, “Properties preserved under homomorphism,” Pacific J. Math.,9, No. 1 (1959).

  19. A. Horn, “On sentences which are true of direct unions of algebrans” J. Symb. Logic,16 (1951).

  20. V. F. Krotov and V. I. Gurman, Methods and Problems of Optimal Control [in Russian], Nauka, Moscow (1973).

    Google Scholar 

  21. A. I. Moskalenko, “Sufficient conditions of joint optimality of systems,” Dokl. Akad. Nauk SSSR,232, No. 3, Moscow (1977).

  22. N. Rush, “Sufficient conditions of stability based on global lemmas,” Proceedings of Fifth International Conference on Nonlinear Vibrations (Kiev, 1969) [in Russian], Vol. 2, Izd. IM AN UkrSSR, Kiev (1970).

    Google Scholar 

  23. V. Lakshmikantham and S. Leela, “Global results and stability of motion,” Al. I. Cuza, No. 1, Iasi (1971).

  24. V. M. Matrosov, L. Yu. Anapol'skii, and S. N. Vasil'ev, The Comparison Method in the Mathematical Theory of Systems [in Russian], Nauka, Novosibirsk (1979).

    Google Scholar 

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Authors
  1. V. M. Matrosov
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  2. S. N. Vasil'ev
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  3. V. G. Karatuev
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  4. M. A. Novikov
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  5. E. A. Sumenkov
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  6. S. A. Yadykin
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Additional information

Translated from Kibernetika, No. 2, pp. 27–36, March–April, 1979.

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Matrosov, V.M., Vasil'ev, S.N., Karatuev, V.G. et al. Machine deduction of theorems on dynamic properties with vector functions of Lyapunov. Cybern Syst Anal 15, 184–194 (1979). https://doi.org/10.1007/BF01069328

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  • DOI: https://doi.org/10.1007/BF01069328

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