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Gelig, Arkadii Khaimovich
(1931–2021)
Statistics Math-Net.Ru
Total publications: 47
Scientific articles: 46

Number of views:
This page:2290
Abstract pages:8643
Full texts:3541
References:517
Gelig, Arkadii Khaimovich
Professor
Doctor of physico-mathematical sciences (1984)
Speciality: 01.02.01 (Theoretical mechanics)
Birth date: 12.10.1931
Website: https://www.math.spbu.ru/user/gelig
Keywords: control theory; sampled-data systems; stability of control systems; periodical solutions.

Subject:

Scientific interests concern mathematical problems of control theory, including: stability and oscillations of nonlinear sampled-data systems (systems with a pulse modulation); stability of nonlinear systems with discontinuous nonlinearities.

Biography

Graduated from Faculty of Mathematics and Mechanics of Leningrad (now St. Petersburg) State University in 1955 (Department of Differential Equations). Ph.D. thesis was defended in 1961. D.Sc. thesis was defended in 1984. A list of my works contains more than 140 titles, including 4 monographs.
   
Main publications:
  • Gelig A. Kh., Churilov A. N. Stability and Oscillations of Nonlinear Pulse-Modulated Systems. Boston: Birkhauser, 1998. 362 p.

https://www.mathnet.ru/eng/person17640
List of publications on Google Scholar
https://zbmath.org/authors/?q=ai:gelig.a-kh
https://mathscinet.ams.org/mathscinet/MRAuthorID/218599
https://elibrary.ru/author_items.asp?authorid=2884

Publications in Math-Net.Ru Citations
2018
1. A. Kh. Gelig, I. E. Zuber, “Multidimensional output stabilization of a certain class of uncertain systems”, Avtomat. i Telemekh., 2018, no. 9,  3–17  mathnet  elib; Autom. Remote Control, 79:9 (2018), 1545–1557  isi  scopus 2
2016
2. A. Kh. Gelig, I. E. Zuber, M. S. Zakharenkov, “New classes of stabilizable uncertain systems”, Avtomat. i Telemekh., 2016, no. 10,  93–108  mathnet  elib; Autom. Remote Control, 77:10 (2016), 1768–1780  isi  scopus 2
2012
3. A. Kh. Gelig, I. E. Zuber, “Using the direct and indirect control to stabilize some classes of uncertain systems. II. Pulse and discrete systems”, Avtomat. i Telemekh., 2012, no. 9,  72–87  mathnet  zmath; Autom. Remote Control, 73:9 (2012), 1498–1510  isi  scopus 4
4. A. Kh. Gelig, I. E. Zuber, “Using the direct and indirect control to stabilize some classes of uncertain systems. I. Continuous systems”, Avtomat. i Telemekh., 2012, no. 8,  76–90  mathnet; Autom. Remote Control, 73:8 (2012), 1337–1349  isi  scopus 3
2011
5. A. H. Gelig, I. E. Zuber, “Invariant stabilization of classes of uncertain systems with delays”, Avtomat. i Telemekh., 2011, no. 9,  161–172  mathnet  mathscinet  zmath; Autom. Remote Control, 72:9 (2011), 1941–1950  isi  scopus 6
2009
6. A. Kh. Gelig, I. E. Zuber, “Vector control design for robust stabilization of a class of uncertain systems”, Avtomat. i Telemekh., 2009, no. 11,  117–125  mathnet  mathscinet  zmath; Autom. Remote Control, 70:11 (2009), 1871–1879  isi  scopus 6
7. A. Kh. Gelig, I. E. Zuber, “Robust stabilization of continuous indeterminate systems”, Avtomat. i Telemekh., 2009, no. 2,  101–108  mathnet  mathscinet  zmath; Autom. Remote Control, 70:2 (2009), 263–270  isi  scopus 2
2007
8. A. Kh. Gelig, I. E. Zuber, “Stability of quasistationary systems”, Avtomat. i Telemekh., 2007, no. 6,  24–34  mathnet  mathscinet  zmath  elib; Autom. Remote Control, 68:6 (2007), 954–963  elib  scopus
2006
9. A. Kh. Gelig, A. N. Churilov, “Frequency methods in the theory of pulse-modulated control systems”, Avtomat. i Telemekh., 2006, no. 11,  60–76  mathnet  mathscinet  zmath; Autom. Remote Control, 67:11 (2006), 1752–1767  scopus 6
2004
10. A. Kh. Gelig, I. E. Zuber, “Stabilization of nonstationary pulse systems”, Avtomat. i Telemekh., 2004, no. 5,  29–37  mathnet  mathscinet  zmath; Autom. Remote Control, 65:5 (2004), 712–720  isi  scopus
2002
11. A. Kh. Gelig, “Asymptotic Stability of Nonlinear Pulse Systems”, Avtomat. i Telemekh., 2002, no. 8,  13–21  mathnet  mathscinet  zmath; Autom. Remote Control, 63:8 (2002), 1217–1224  isi  scopus 1
1998
12. A. Kh. Gelig, “Stability of asynchronous impulse systems with random perturbations of parameters”, Avtomat. i Telemekh., 1998, no. 5,  181–185  mathnet  mathscinet  zmath; Autom. Remote Control, 59:5 (1998), 757–760 1
1997
13. A. Kh. Gelig, A. N. Churilov, “On stability in the large of systems with impulse action”, Differ. Uravn., 33:6 (1997),  748–753  mathnet  mathscinet; Differ. Equ., 33:6 (1997), 752–756
1996
14. A. Kh. Gelig, “Robust Stabuity of Nonlinear Impulse Systems”, Avtomat. i Telemekh., 1996, no. 12,  78–83  mathnet  mathscinet  zmath; Autom. Remote Control, 57:12 (1996), 1753–1758 1
15. N. E. Barabanov, A. Kh. Gelig, G. A. Leonov, A. L. Likhtarnikov, A. S. Matveev, V. B. Smirnova, A. L. Fradkov, “The Frequency Theorem (Kalman–Yakubovich Lemma) in Control Theory”, Avtomat. i Telemekh., 1996, no. 10,  3–40  mathnet  mathscinet  zmath; Autom. Remote Control, 57:10 (1996), 1377–1407 31
1995
16. A. Kh. Gelig, Yu. V. Elkhimova, “Stability of nonlinear pulse systems in the presence of random disturbances of parameters”, Avtomat. i Telemekh., 1995, no. 11,  140–147  mathnet  mathscinet  zmath; Autom. Remote Control, 56:11 (1995), 1620–1626 2
17. A. Kh. Gelig, A. N. Churilov, “Periodic regimes in systems with frequency-impulse modulation of the second type”, Avtomat. i Telemekh., 1995, no. 10,  86–93  mathnet  mathscinet  zmath; Autom. Remote Control, 56:10 (1995), 1425–1431
18. A. Kh. Gelig, A. N. Churilov, “Periodic modes in pulse-frequency systems”, Avtomat. i Telemekh., 1995, no. 7,  91–98  mathnet  mathscinet  zmath; Autom. Remote Control, 56:7 (1995), 982–988 1
1993
19. E. Yu. Aĭvazyan, A. Kh. Gelig, “Stability of asynchronous impulse systems with combined modulation”, Avtomat. i Telemekh., 1993, no. 4,  108–114  mathnet  mathscinet  zmath; Autom. Remote Control, 54:4 (1993), 624–631
20. A. Kh. Gelig, Yu. V. Elkhimova, “The averaging method in the dynamics of nonlinear impulse systems”, Izv. Vyssh. Uchebn. Zaved. Mat., 1993, no. 4,  58–61  mathnet  mathscinet  zmath; Russian Math. (Iz. VUZ), 37:4 (1993), 55–58
1990
21. A. Kh. Gelig, A. N. Churilov, “Periodical regimes in impulse-modulated systems with variable structure linear component”, Avtomat. i Telemekh., 1990, no. 12,  94–104  mathnet  mathscinet  zmath; Autom. Remote Control, 51:12 (1990), 1683–1692 1
22. A. Kh. Gelig, “Stabilization of impulse systems by periodic external action”, Avtomat. i Telemekh., 1990, no. 4,  76–85  mathnet  mathscinet  zmath; Autom. Remote Control, 51:4 (1990), 485–493
1989
23. A. Kh. Gelig, A. N. Churilov, “Investigating $\Omega$-periodic modes in pulse width systems”, Avtomat. i Telemekh., 1989, no. 2,  30–39  mathnet  mathscinet  zmath; Autom. Remote Control, 50:2 (1989), 152–160 1
1988
24. A. Kh. Gelig, N. I. L'yanova, “A circular criterion for stability of nonlinear sampled-data systems with a new kind of quadratic relations”, Avtomat. i Telemekh., 1988, no. 6,  33–39  mathnet  mathscinet  zmath; Autom. Remote Control, 49:6 (1988), 714–719
25. A. Kh. Gelig, O. Ya. Karetnyi, M. L. Yudkevich, “Stability of processes and extreme limit in pulse-width modulated systems”, Avtomat. i Telemekh., 1988, no. 5,  31–41  mathnet  mathscinet  zmath; Autom. Remote Control, 49:5 (1988), 570–579
1986
26. A. Kh. Gelig, A. N. Churilov, “Periodic modes in pulse-width modulation systems”, Avtomat. i Telemekh., 1986, no. 11,  37–44  mathnet  zmath; Autom. Remote Control, 47:11 (1986), 1490–1497 1
1984
27. A. Kh. Gelig, “Natural oscillations in sampled data systems with a high clock frequency”, Avtomat. i Telemekh., 1984, no. 10,  23–29  mathnet  mathscinet  zmath; Autom. Remote Control, 45:10 (1984), 1262–1268
1983
28. A. Kh. Gelig, “The averaging method in the stability theory of nonlinear sampled data systems”, Avtomat. i Telemekh., 1983, no. 5,  55–64  mathnet  mathscinet  zmath; Autom. Remote Control, 44:5 (1983), 591–600
1980
29. A. Kh. Gelig, “Dissipativity of pulse-width systems with high time base frequency”, Avtomat. i Telemekh., 1980, no. 11,  54–60  mathnet  zmath; Autom. Remote Control, 41:11 (1981), 1523–1529
1979
30. N. A. Antonova, A. Kh. Gelig, “Stability of integral pulse-width modulation systems”, Avtomat. i Telemekh., 1979, no. 10,  51–57  mathnet  mathscinet  zmath; Autom. Remote Control, 40:10 (1980), 1442–1447
1978
31. A. Kh. Gelig, Yu. Ya. Morgovskii, “Stability of one class of variable structure systems and nonautonomous pulse shaping”, Avtomat. i Telemekh., 1978, no. 2,  36–41  mathnet  zmath; Autom. Remote Control, 39:2 (1978), 184–189
32. A. Kh. Gelig, Yu. Ya. Morgovskii, “Sampled-data systems with frequency to phase conversion and internal reset in the modulator”, Avtomat. i Telemekh., 1978, no. 1,  68–74  mathnet  zmath; Autom. Remote Control, 39:1 (1978), 51–57
33. A. Kh. Gelig, “Stability of pulse-width systems of phase synchronization”, Sibirsk. Mat. Zh., 19:1 (1978),  19–27  mathnet  mathscinet  zmath; Siberian Math. J., 19:1 (1978), 12–19  isi
1977
34. Z. U. Blyagoz, A. Kh. Gelig, “A pulse-width synchronization system”, Avtomat. i Telemekh., 1977, no. 8,  55–60  mathnet  zmath; Autom. Remote Control, 38:8 (1977), 1157–1161
1976
35. A. Kh. Gelig, Yu. Ya. Morgovskii, “Stability of the stationary state of systems with nonautonomous pulse generation and phase modulation of the second kind”, Avtomat. i Telemekh., 1976, no. 11,  63–69  mathnet  mathscinet  zmath; Autom. Remote Control, 37:11 (1976), 1680–1686
36. A. Kh. Gelig, Yu. Ya. Morgovskii, “Absolute stability of system with nonautonomous pulse generation and phase modulation of the first kind”, Avtomat. i Telemekh., 1976, no. 10,  41–47  mathnet  zmath; Autom. Remote Control, 37:10 (1976), 1504–1510
37. A. Kh. Gelig, Yu. Ya. Morgovskii, “Sampled-data systems with frequency phase conversion”, Avtomat. i Telemekh., 1976, no. 5,  74–80  mathnet  mathscinet  zmath; Autom. Remote Control, 37:5 (1976), 706–712
1975
38. N. A. Antonova, A. Kh. Gelig, “Stability of periodic modes in pulse-width systems”, Avtomat. i Telemekh., 1975, no. 7,  38–46  mathnet  mathscinet  zmath; Autom. Remote Control, 36:7 (1975), 1083–1091
39. N. A. Antonova, A. Kh. Gelig, “Stability of processes in pulse-width modulation sampled-data systems”, Avtomat. i Telemekh., 1975, no. 6,  64–72  mathnet  mathscinet  zmath; Autom. Remote Control, 36:6 (1975), 932–940
1972
40. A. Kh. Gelig, “The stability of relay systems”, Differ. Uravn., 8:9 (1972),  1684–1686  mathnet  mathscinet  zmath
1969
41. A. Kh. Gelig, “Stability of pulse systems with frequency modulation”, Dokl. Akad. Nauk SSSR, 185:2 (1969),  253–256  mathnet  mathscinet  zmath
1968
42. A. Kh. Gelig, “The stability of nonlinear pulse systems”, Dokl. Akad. Nauk SSSR, 178:4 (1968),  793–796  mathnet  mathscinet  zmath 1
1962
43. A. Kh. Gelig, “Stability of motion of systems without a unique equilibrium position”, Dokl. Akad. Nauk SSSR, 147:3 (1962),  526–528  mathnet  mathscinet  zmath
1960
44. A. Kh. Gelig, “Stability of the solutions of a mixed problem for a hyperbolic equation of second order”, Izv. Vyssh. Uchebn. Zaved. Mat., 1960, no. 3,  104–112  mathnet  mathscinet  zmath
45. A. Kh. Gelig, “Stability of the solutions of the Cauchy problem for symmetric systems of partial differential equations”, Izv. Vyssh. Uchebn. Zaved. Mat., 1960, no. 1,  69–83  mathnet  mathscinet  zmath
1958
46. A. Kh. Gelig, “The stability of the solutions of Cauchy problem and the mixed problem for hyperbolic equations”, Dokl. Akad. Nauk SSSR, 123:4 (1958),  591–594  mathnet  mathscinet  zmath
2006
47. A. Kh. Gelig, G. A. Leonov, A. L. Fradkov, “Vladimir Andreevich Yakubovich”, Avtomat. i Telemekh., 2006, no. 10,  4–19  mathnet  mathscinet  zmath  elib; Autom. Remote Control, 67:10 (2006), 1530–1546 4

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