Extension of Popov absolute stability criterion to non-autonomous systems with delays

International Journal of Control

Volumn 73, Issue 15, 2000, Pages 1349-1361

  Bliman, Pierre Alexandre ^a  

^a INRIA   (France)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; FREQUENCY DOMAIN ANALYSIS; GRAPHIC METHODS; MATRIX ALGEBRA; MULTIVARIABLE CONTROL SYSTEMS; NONLINEAR CONTROL SYSTEMS; ROBUSTNESS (CONTROL SYSTEMS);

NON-AUTONOMOUS SYSTEMS;

DELAY CONTROL SYSTEMS;

EID: 0034668347     PISSN: 00207179     EISSN: None     Source Type: Journal    
DOI: 10.1080/002071700445370     Document Type: Article

References (39)

1. Aizerman, M.A., 1947, On the effect of nonlinear functions of several variables on the stability of automatic control problems. Avtomat. i telemeh. 8, 20-29 (Russian).
2. Aizerman, M.A., and Gantmacher, F.R., 1964, Absolute Stability of Regulator Systems (Holden-Day Inc.).
3. Barabanov, N.E., 1989, New frequency criteria for absolute stability and instability of automatic-control systems with nonstationary nonlinearities. Differential Equations, 25, 367-373.
4. Barabanov, N.E., Gelig, A. Kh., Leonov, G.A., Likhtarmkov, A.L., MATVEEV, A.S., SMIRNOVA, V.B., and FRADKOV, A.L., 1997, The frequency theorem (the Yakubovic-Kalman lemma) in control theory. Automation and Remote Control, 57, 1377-1407.
5. Bertoni, G., Bonivento, C., and Sarti, E., 1969/1970, A graphical method for investigating the absolute stability of time-varying systems. Atti Accad. Sci. Ist. Bologna Cl. Sci. Fis. Redn. (12) 7, fasc. 1, 54-71.
6. Bliman, P.-A., 1999a, Delay-independent criterion of absolute stability for nonautonomous systems variable delays. Modern applied mathematics in circuits, systems and control. Proceedings of the IMCAS/IEEE CSCC'99, Athens, Greece, World Scientific Engineering Socity.
7. Bliman, P.-A., 1999 b, Absolute stability of nonautonomous delay systems: delay-dependent and delay-independent criteria. Proceedings of the 38th IEEE Conference on Decision and Control, Phoenix (Arizona), 2005-2010.
8. Boyd, S., El Ghaoui, L., Feron, E., and Balakrishnan, V., 1994, Linear matrix inequalities in system and control theory. SlAM Studies in Applied Mathematics, 15.
9. Corduneanu, C., 1972, Absolute stability of some integro-differential systems. Ordinary Differential Equations (Proc. Conf., Math. Res. Center, Naval Res. Lab., Washington, D.C., 1971) (New York: Academic Press) pp. 55-70.
10. Fradkov, A.L., and Pogromsky, A. Yu., 1998, Introduction to Control of Oscillation and Chaos (World Scientific Publishers).
11. Grujić, Lj.T., Borne, P., and Gentina, J.C., 1979, Matrix approaches to the absolute stability of time-varying Lurie-Postnikov systems. International Journal of Control, 30, 967-980.
12. Halanay, A., 1966, Differential equations: stability, oscillations, time lags (New York-London: Academic Press).
13. Halanay, A., and Rasvan, V.L., 1981, Approximations of delays by ordinary differential equations. In R. Conti (ed.) Recent Advances in Differential Equations (New York-London: Academic Press), pp. 155-197.
14. Hul'chuk, H.H., and Lychak, M.M., 1972, Absolute stability of nonlinear control systems with nonstationary non-linearities and tachometer feedback. Soviet Automatic Control, 5, 6-9.
15. Khalil, H.K., 1992, Nonlinear Systems (Macmillan Publishing Company).
16. Leonov, G.A., 1981, Extension of Popov's frequency criterion for nonstationary nonlinearities. Automation and Remote Control, 41, 1494-1499.
17. Leonov, G.A., Burkin, I.M., and Shepelhavyi, A.I., 1996, Frequency Methods in Oscillation Theory (Kluwer).
18. Li, X.-J., 1963, On the absolute stability of systems with time lags. Chinese Mathematics, 4, 609-626.
19. Liao, X.X., 1993, Absolute Stability of Nonlinear Control Systems, Mathematics and its Applications (Chinese Series) 5 (Dordrecht: Kluwer Academic/Beijing: Science Press).
20. Liberzon, M.R., 1980, New results on absolute stability of nonstationary controlled systems (survey). Automation and Remote Control, 40, 1124-1140.
21. Liberzon, M.R., 1989, The inner feature of absolute stability of nonstationary systems. Automation and Remote Control, 50, 608-613.
22. Narendra, K.S., and Taylor, J.H., 1973, Frequency Domain Criteria for Absolute Stability (New York-London: Academic Press).
23. ∝ approximation and nuclearity of delay systems. Systems Control Letters, 10, 59-65.
24. Pliss, V.A., 1958, Certain Problems in the Theory of Stability in the Whole (Leningrad State University) (Russian).
25. Popov, V.M., 1961, Absolute stability of nonlinear systems of automatic control. Automation and Remote Control, 22, 857-875.
26. Popov, V.M., and Halanay, A., On the stability of nonlinear automatic control systems with lagging argument. Automatic Remote Control, 23, 783-786.
27. Pyatnitskii, E.S., 1970, Absolute stability of nonstationary nonlinear systems. Automation and Remote Control, 1, 1-9.
28. Pyragas, K., 1992, Continuous control of chaos by self-controlling feedback. Physics Letters A, 170, 421-428.
29. Pyragas, K., 1995, Control of chaos via extended delay feed-back. Physics Letters A, 206, 323-330.
30. Rantzer, A., 1996, On the Kalman-Yakubovich-Popov lemma. Systems Control Letters, 28, 7-10.
31. Rasvan, Vi., 1972, Frequency domain stability criteria for time lag control systems with several nonlinearities. III. Linear and nonlinear systems with monotonic time varying gain. Rev. Roumaine Sci. Tech. Sér. Électrotech. Énergét., 17, 507-521.
32. Rekasius, Z.V., and Gibson, J.E., 1962, Stability analysis of nonlinear control systems by the second method of Lyapunov. IRE Transactions on Automatic Control, AC-7, 3-15.
33. Rekasius, Z.V., and Rowland, J.R., 1965, A stability criterion for feedback systems containing a single time-varying nonlinear element. IEEE Transactions on Automatic Control, 352-354.
34. Rockafellar, R.T., 1970, Convex Analysis, Princeton Mathematical Series No. 28 (Princeton University Press).
35. Rudin, W., 1987, Real and Complex Analysis, 3rd edn (McGraw-Hill).
36. Walker, J.A., 1967, Stability of feedback systems involving time dealys and a time-varying nonlinearity. International Journal of Control, 6, 365-372.
37. Walker, J.A., 1968, Liapunov functions for feed-back systems containing a single time-varying nonlinearity. International Journal of Control, 7, 171-174.
38. Willems, J.L., 1970, Stability Theory of Dynamical Systems (Thomas Nelson and Sons Ltd).
39. Yakubovich, V.A., 1965, The method of matrix inequalities in the theory of stability of non-linear controlled systems. III. Absolute stability of systems with hysteresis non-linearities. Automation and Remote Control, 26, 753-763.