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Foundations of Differential and Topological Diagnostics

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REFERENCES

  1. P. P. Parkhomenko and E. S. Sagomonyan, Found tions of Engineering Diagnostics [in Russian ], Energiya, Moscow (1981).

    Google Scholar 

  2. V. V. Karibskii, P. P. Park omenko, E. S. Sagomonyan, and V. F. Khalchev, Foundations of Engi-neering Diagnostics. Book 1 [in Russian ], Energiya, Moscow (1976).

    Google Scholar 

  3. L. A. Mironovskii, "Functional diagnostics of dynamical systems, "Avtom. Telemekh., No. 3, 96-121 (1980).

    Google Scholar 

  4. A. V. Maiorov, G. K. Moskatov, and G. P. Shibanov, Safety in Operation of Automated Plants [in Russian ], Mas inostroenie, Moscow (1988).

    Google Scholar 

  5. B. N. Petrov, V. J. Rutkovskij, I. N. Krutova, and Zemlyakov S. D., Principles of Construction and Design of Self-Adapting Control Systems [in Russian ], Mas inostroenie, Moscow (1972).

    Google Scholar 

  6. V. J. Rutkovskii, S D. Zemlyakov, V. M. Glumov, et al. "Adaptive algorithmic methods for diag-nostics and faultless operation of control systems, "In: Proc. 3rd IMECO Symposium on Technic l Diagnostics, Moscow, 1983. Budapest, Publ. IMECO (1985), pp. 173-180.

    Google Scholar 

  7. I. T. Borisenok, "Redundant control systems, "in Proc. 3rd All-Union Conf. on Control Systems (Engeneering Cybernetics )[in Russian ], Odessa (1963).

  8. I. T. Borisenok, "On the differential restorability t eory. Certain control and stability problems for mec anical systems, "P pers of the Institute of Mechanics of Lomonosov Moscow State University Issue 22 [in Russian ], Izd. Mosk. Gos. Univ., 101-108 (1973).

  9. M. Eykhoff., Foundations of Control System Identi cation [Russian translation], Mir, Moscow (1975).

    Google Scholar 

  10. V. I. Belyakov and I. T. Borisenok. "Modeling methods using the list of probable flaws in functional diagnostics of dynamical systems, "VIII Symp. on Problems of D t System Redund ncy. Abstract of Papers. Leningrad (1983), Part 3.

  11. V. I. Belyakov, I. T. Borisenok, and V. A. Samsonov, "On an algorithm for continuous express-diagnostics, "Avtomat. Telemekh., No. 3, 113-116 (1973).

    Google Scholar 

  12. V. I. Belyakov and I. T. Borisenok, "On a method for the construction of a c ecking surface in the diagnostic problem, "Certain Problems of Dynamics of Controlled Rigid Bodies. Collection of Papers [in Russian ], Izd. Mosk. Gos. Univ., Moscow (1982).

    Google Scholar 

  13. I. T. Borisenok and B. Ya. Loks in, "On t e problem of system diagnostics, "All-Union Symp. on Diagnostic System Design. Abstracts of Papers [in Russian ], Rostov-on-Don, May 1978.

  14. I. T. Borisenok and I. A. Smarz evskii, "Diagnostics of a certain directly controlled system, " In: Readings in Memory of V. N. Chelomei. Abstr cts of Papers [in Russian ], Moscow, Institute of Engineering Science, USSR Academy of Sciences, June 1989.

    Google Scholar 

  15. Yu. M. Okunev and N. A. Parusnikov, Structural and Algorithmic Aspects of the Set-Up of Control Problems [in Russian ], Izd. Mosk. Gos. Univ., Moscow (1983).

    Google Scholar 

  16. I. T. Borisenok and I. A. Smarz evskii, N vig tion and Control Theory for Moving Objects. Tech-niques for Functional Diagnostics of an Aircaft 's Motion Control System. Rese rch Report No. 3930. Institute of Mechanics of Lomonosov Moscow State University [in Russian ], Izd. Mosk. Gos. Univ., Moscow (1990).

    Google Scholar 

  17. I. T. Borisenok and A. G. Shakot 'ko, Design of Control nd Diagnostic Algorithms for Aerosp ce Systems. Research Report No. 4173. Institute of Mechanics of Lomonosov Moscow State University. [in Russian ], Izd. Mosk. Gos. Univ., Moscow (1992).

    Google Scholar 

  18. E. A. Barbas in, An Introduction to Stability Theory [in Russian ], Nauka, Moscow (1967). 1023.

    Google Scholar 

  19. V. V. Nemytskii and V. V. Stepanov, The Qualitative Theory of Differential Equations [in Russian ], Gostek izdat, Moscow (1949).

    Google Scholar 

  20. N. Minorsky, "Directional stability of automatically steered bodies, "J. Soc. Naval Endrs (May, 1922).

  21. S. Lefschets, Differential Equations: Geometric Theory, 2nd ed., Wiley, Interscience, New York (1963).

    Google Scholar 

  22. S. Lefschets, The Geometric Theory of Differential Equations [Russian translation], Inostrannaya Literatura, Moscow (1961).

    Google Scholar 

  23. M. G. Chikin, "State-constrained systems, "Avtomat. Telemekh., No. 10, 38-46 (1987).

    Google Scholar 

  24. V. P. Zhukov, "On the necessary and sufficient conditions for asymptotic stability of nonlinear dynamical systems, "Avtomat. Telemekh., No. 3, 24-36 (1994).

    Google Scholar 

  25. A. V. Bogatyrev and E. S. Pyatnitskii, "T e construction of piecewise quadratic Lyapunov functions for nonlinear control systems, "Avtomat. Telemekh., No. 10, 30-38 (1987).

    Google Scholar 

  26. V. P. Chistyakov. A Course on Probability Theory [in Russian ], Nauka, Moscow (1987).

    Google Scholar 

  27. I. T. Borisenok and V. I. Belyakov, "T e construction of areas of tolerable deviations for c ecking problems, "in IV All-Union Conf. on Engineering Diagnostics. Cherkassy, 1979. Abstr cts of Papers [in Russian ], Part 2, pp. 24-26, Moscow (1979).

  28. I. T. Borisenok and V. I. Belyakov, "T e construction of tubes for checking the glideslope motion, " in: IInd All-Union Scientific and Technologic l Conf. on Flight Safety and Optimal Operation of Air Tr nsportation Systems. Abstr cts of Papers [in Russian ], Leningrad (1979), pp. 46-47.

  29. V. I. Blagodatskikh and A. P. Philippov, "Differential inclusions and optimal control, " In: Topol ogy, Ordinary Differential Equations, and Dynamical Systems. Collection of Papers. Dedicated to the Institute's 50th Anniversary. Part 2, Trudy MIAN SSSR, 169, Nauka, Moscow (1985), pp. 194-252.

    Google Scholar 

  30. I. Babushka, E. Vitasek, and M. Praguer, Solving Differential Equations Numerically [Russian trans-lation ], Mir, Moscow (1969).

    Google Scholar 

  31. B. V. Gnedenko, A Course on Prob bility Theory [in Russian ], Nauka, Moscow (1963).

    Google Scholar 

  32. D. Hudson, Statistic l Theory for Physicists [Russian translation ], Mir, Moscow (1970).

    Google Scholar 

  33. L. S. Gutkin, Theory of Optimal Techniques for Radio Reception through Fluctuation Noise [in Russian ], Moscow (1972).

  34. B. R. Levin, Theoretic l Foundations of Statistic l Radio Engineering [in Russian ], Moscow (1989).

  35. B. V. Bulgakov, Oscill tions [in Russian ], Moscow (1954).

  36. A. M. Letov, Stability of Nonlinear Controllable Systems [in Russian ], Fizmatgiz, Moscow (1962).

    Google Scholar 

  37. S. Lefschets, Stability of Nonlinear Automatic Control Systems [Russian translation ], Mir, Moscow (1967).

    Google Scholar 

  38. I. T. Borisenok and M. V. Shamolin, "Solution algorithms for the problem of differential diagnostics, " In: Abstr cts of Papers. 3rd Erugin 's Readings Mathematic l Conf. (Brest, May 14-16, 1996) [in Russian ] Brest, 1996, p. 102.

  39. I. T. Borisenok and M. V. Shamolin. "The existence and uniqueness of a solution to the general problem of differential diagnostics, "In: 5th Intern. Conf on Physical and Engineering Problems of Advanced Engineering Systems (Moscow, May 19-22, 1998)[in Russian ] Izd. Mosk. Gos. Tekh. Univ., Moscow (1998), pp. 6-7.

    Google Scholar 

  40. I. T. Borisenok and M. V. Shamolin, "Solution to the problem of differential diagnostics, "Fundamental Applied Mathematics (to appear).

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Shamolin, M.V. Foundations of Differential and Topological Diagnostics. Journal of Mathematical Sciences 114, 976–1024 (2003). https://doi.org/10.1023/A:1021807110899

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