Absolute stability of dynamical systems (Survey)

IFAC Proceedings Volumes (IFAC-PapersOnline)

Volumn 15, Issue 1, 2002, Pages 37-42

  Liberzon, Mark R ^a  

^a MOSCOW AVIATION INSTITUTE NATIONAL RESEARCH UNIVERSITY   (Russian Federation)

Author keywords

Absolute stability; Dynamical system; Lur'e problem

Indexed keywords

AUTOMATION; DYNAMICAL SYSTEMS; SURVEYS;

ABSOLUTE STABILITY; LUR'E PROBLEM;

SYSTEM STABILITY;

EID: 84945568938     PISSN: 14746670     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.3182/20020721-6-es-1901.00256     Document Type: Conference Paper

References (55)

1. Aizerman, M.A. (1949). About one problem concerning the stability "in large" of dynamic systems. Uspekhi Matem. Nauk, 4, 186-188.
2. Aizerman, M.A. and Gantmacher, F.R. (1963). Absolute stability of regulation systems. Acad. Nauk SSSR - Press (In Russian, English transi. SF: Holden Day, 1964).
3. Aizerman, M.A. (1966). Theory of Automatic Control. Moscow, Nauka.
4. Aleksandrov, V.V. and Zhermolenko, V.N. (1975). A criterion for absolute stability of third-order systems. Doklady Akad. Nayk SSSR, 222, pp. 309-311.
5. Barabanov, N.E. (1982). Existence of periodic solutions of nonlinear controlled systems and the Kalman's hypothesis. Uspekhi Matem. Nauk, 37, No. 1, p. 164.
6. Barabanov, N.E. (1988a). On the absolute stability problem for impulse control systems. Avtomatika i Telemekhanika
7. Barabanov, N.E. (1988b). About the Kalman's hypothesis. Sibirsky Matem. Zhurnal, No. 3.
8. Barabanov, N.E., Gelig, A. Kh., Leonov, G.A., Likhtarnikov, A.L., Matveev, A.S., Smirnova, V.B. and Fradkov, A.L. (1996). The frequency theorem (Kalman-Yakubovich lemma) in control theory. Avtomatika i Telemekhanika, 57, No. 10, pp. 3-40.
9. Beklemishev, N.N. and Liberzon, M.R. (1993). The Use of Inner Method in Stability Analysis of Control Systems for Special Technological Processes. In: Fundamentals of Discrete-Time Systems, Albuquerque, New Mexico, USA, TSI Press, pp. 189-194.
10. Bliman, P.-A. (1999). Extension of Popov criterion to time-varying nonlinearities: LMI, frequential and grafical conditions. In: Stability and stabilization of nonlinear systems (Ghent, 1999), pp. 95-114, Lecture Notes in Control and Inform. Sci., 246, Springer, London.
11. Bulgakov, B.V. (1942). Auto oscillations of controlled systems. Dokladi Akad. Nauk SSSR, 37, 283-287.
12. Bulgakov, B.V. (1946). Some problems of the control theory with nonlinear characteristics. Prikl. Mat: Mekh, 10, 313-332.
13. Fitts, R.E. (1966). Two counterexamples to Aizerman's conjecture. IEEE Trans. On Autom. Control AC-11, pp. 553-556.
14. Gelig, A. Kh., Leonov, G.A. and Yakubovich, V.A. (1978). Stability of Nonlinear Systems With Nonsingular Balance Position. Nauka, Moscow.
15. Harris, C.J. and Valenca, J.M.E. (1983). The Stability of Input-Output Dynamical Syatems. Acad. Press, Math. In Sci. And Eng., 168.
16. Jury, E.I. (1974). Inners and Stability of Dynamic Systems. Wiley (Second Edition in 1982).
17. Kalman, R.E. (1957). Physical and mathematical mechanisms of instability in nonlinear automatic control systems. Trans. ASME, 79, 553-566.
18. Kalman, R.E. (1963). Liapunov functions for the Problem of Lurie in automatic control. Proc. Nat. Acad. Sci. USA, 49, pp. 201-205.
19. Kamenetsky, V.A. and Pyatnitsky, E.S. (1987). Gradient method for constructing of Lyapunov functions in the absolute stability problems. Avtomatika Telemekhanika, No. 1, pp. 3-12.
20. Kuntsevich, V.M. and Lychak, M.M. (1977). Synthesis of Automatic Control Systems With Help of the Lyapunov Function. Nauka, Moscow.
21. La Salle, J. and Lefschetz, S.L. (1961). Stability by Liapunov's Direct Method. Acad. Press, New York, London.
22. Lefschetz, S.L. (1965). Stability of Nonlinear Control Systems. Academic Press, New York - London.
23. Letov, A.M. (1955). Stability of Nonlinear Controlled Systems. Gostekhizdat (In Russian).
24. Liberzon, M.R. (1979). New results on absolute stability of nonstationary controlled systems (survey). Avtomatika i Telemekhanika, No. 5, pp. 29-48.
25. Liberzon, M.R. (1986). Criterion of Absolute Stability of Nonstationary Systems. Avtomatika Telemekhanika, No. 2, pp. 39-46.
26. Liberzon, M.R. (1989a). An Inners Criterion of Absolute Sstability of Nonstationary Control Systems. Doklady Akademii Nauk SSSR, 304, No. 5, pp. 1060-1064.
27. Liberzon, M.R. (1989b). Iinner Criterion of Absolute Stability of Nonstationary Systems. Avtomatika i Telemekhanika, No. 5, pp. 40-46.
28. Liberzon, M.R. (1993). Inner Indication of Absolute Stability for Discrete Systems. In: Fundamentals of Discrete-Time Systems, Albuquerque, New Mexico, USA, TSI Press, pp. 333-338.
29. Liberzon, M.R. (1999). On the stability of controlled flight of an axisymmetric rotating vehicle with incomplete model information. Proc. 1999 American Control Conference, 5, pp. 3520-3524, San Diego, CA, USA.
30. th IFAC Symposium "Nonlinear Control Systems NOLCOS'01", 1, pp. 22-25, Saint-Petersburg, Russia.
31. Lur'e, A.L, and V.M. Postnikov (1944). On the theory of stability of controlled systems. Prikl. Mat.i Mekh, 8, 283-286.
32. Lur'e, A.L. (1951). Certain Nonlinear Problems in the Automatic Regulating Theory. Gostekhizdat (In Russian, English Transi.: London, HMSO, 1975).
33. Molchanov, A.P. (1979). Absolute stability of impulse systems with a number of nonlinear nonstationary elements. Avtomatika i Telemekhanika, No. 3, pp. 43-51.
34. Molchanov, A.P. (1983). Absolute stability criterion for impulse systems with nonstationary nonlinearity. Avtomatika i Telemekhanika, No. 5, pp. 73-81; No. 6, pp. 42-52.
35. Molchanov, A.P. and Pyatnitsky, E.S. (1986). Lyapunov functions which define necessary and sufficient conditions of absolute stability for nonlinear nonstationary control systems. Avtomatika Telemekhanika, No. 3, pp. 63-73; No. 4, pp. 5-15; No. 5, pp. 38-49.
36. Narendra, K.S. and Taylor, J.H. (1973). Frequency Domain Criteria for Absolute Stability. Acad. Press, New York.
37. Naumov, B.N. (1972). Theory of Nonlinear Automatic Systems. Nauka, Moscow.
38. Pliss, V.A. (1958). Certain Problems of the Theory of Stability of Motion in the Whole. Leningrad University Press.
39. Popov, V.-M. (1961). On the absolute stability of nonlinear controlled systems. Avtomatika Telemekhanika, No. 8, pp. 961-970.
40. Popov, V.-M. (1973). Hiperstability of Control Systems. Springer-Verlag, New York.
41. Pyatnitsky, E.S. (1968). New research on absolute stability of automatic control systems (survey). Avtomatika i Telemekhanika, No. 6, pp. 5-36.
42. Pyatnitsky, E.S. (1970). Absolute stability of nonstationary nonlinear systems. Avtomatika Telemekhanika, No. 1, pp. 5-15.
43. Pyatnitsky, E.S. (1972). An extention of thje frequency criterion for absolute stability of control system with a single nonlinear nonstationary element. Izvestiya Vuzov, Radiofizika, 15, No. 3, pp. 319-322.
44. Pyatnitsky, E.S. (1973a). On the existence of absolute stability systems, for which the criterion of V.-M. Popov is not satisfied. Avtomatika Telemekhanika, No. 1, pp. 30-37.
45. Pyatnitsky, E.S. (1973b). On uniform stability in the presence of parametric perturbations. Differentsial. Uravneniya, 9, No. 7, pp. 1262-1274.
46. Resvan, V. (1983). Absolute Stability of Control Systems With Time Delay. Nauka, Moscow.
47. Ruitenberg, Ya.N. (1971). Automatic Control. Nauka, Moscow.
48. Shilman, S.V. (1978). Method of Generating Functions in the Theory of Dynamical Systems. Nauka, Moscow.
49. Vidal, P. (1968). Systems Echantillones Nonlineatres. Cordon and Breach Paris.
50. Voronov, A.A. (1966). Fundamentals of the Theory of Automatic Control. Energia Press (Second Ed. In 1981).
51. Voronov, A.A. (1982). Stability theory: state of art and problems. Avtomatika i Telemekhanika, No. 5, pp. 5-28.
52. Yakubovich, V.A. (1962). Solving some matrix inequalities, which are meeting in control theory. Doklady Acad. NaukSSSR, 143, pp. 1304-1307.
53. Yakubovich, V.A. (1967). Frequency conditions of absolute stability of the control systems with some non-linear and linear non-stationary blocks. Avtomatika i Telemekhanika, No. 6, pp. 5-30.
54. Yakubovich, V.A. (1975). Methods of the theory of absolute stability. In: Methods for Investigating Nonlinear Control Systems (R.A. Nelepin, Ed.). Nauka, Moscow.
55. Yakubovich, V.A. (1998). Quadratic criterion of absolute stability. Doklady Acad. Nauk, 361, pp. 608-611.