Oscillation conditions of nonlinear systems with static feedback

Automation and Remote Control

Volumn 66, Issue 1, 2005, Pages 249-264

  Eflmov, D V ^a   Fradkov, A L ^a  

^a INSTITUTE OF PROBLEMS OF MECHANICAL ENGINEERING   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTER SIMULATION; CONTROL SYSTEM ANALYSIS; CONTROL SYSTEM SYNTHESIS; FEEDBACK; LYAPUNOV METHODS; OSCILLATIONS; PROBLEM SOLVING; STATE ESTIMATION; SYSTEM STABILITY; FUNCTIONS; LARGE SCALE SYSTEMS; MATHEMATICAL MODELS; SET THEORY;

LORENTZ SYSTEMS; STATE VECTORS; STATIC FEEDBACK; VAN DER POL SYSTEMS; COMPUTER MODELING; NONLINEAR NOMINAL PORTION;

NONLINEAR CONTROL SYSTEMS; NONLINEAR SYSTEMS;

EID: 17144426138     PISSN: 00051179     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (26)

1. Fradkov, A.L., Miroshnik, I.V., and Nikiforov, V.O., Nelineinoe i adaptivnoe upravlenie slozhnymi dinamicheskimi sistemami (Nonlinear and Adaptive Control of Complex Dynamic Systems), St. Petersburg: Nauka, 2000.
2. Jiang, Z.-R, Teel, A., and Praly, L., Small-Gain Theorem for ISS Systems and Applications, Math. Control Signal Syst., 1994, no.7, pp. 95-120.
3. Sepulchre, R., Jankovic, M., and Kokotivic, P.V., Constructive Nonlinear Control, New York: Springer-Verlag, 1996.
4. Leonov, G.A., Burkin, I.M., and Shepelyavyi, A.I., Chastotnye metody v teorii kolebanii (Frequency Methods in the Theory of Oscillations), St. Petersburg: Nauka, 1992.
5. Martinez, S., Cortes, J., and Bulko, F., Analysis and Design of Oscillatory Control Systems, IEEE Trans. Automat. Control, 2003, vol. 48, no. 7, pp. 1164-1177.
6. Fradkov, A.L., Feedback Resonance in Nonlinear Oscillators, Proc. 5th Europ. Control Conf., Karlsruhe, 1999.
7. Fradkov, A.L., Kiberneticheskaya fizika (Cybernetic Physics), St. Petersburg: Nauka, 2003.
8. Yakubovich, V.A., Frequency Conditions of Self-Oscillations in Nonlinear Systems with One Stationary Nonlinearity, Sib. Mat. Zh., 1973, vol. 14, no. 12, pp. 1100-1129.
9. Yakubovich, V.A., Frequency Conditions of Oscillations in Nonlinear Controllable Systems with One Univalent or Hysteretic Nonlinearity, Avtom. Telemekh., 1975, no. 12, pp. 51-64.
10. Hill, D. and Moylan, P., Dissipative Dynamics Systems. Basic Input-Output and State Properties, J. Franklin Inst. 1980, vol, 309, pp.327-357.
11. Polushin, I.G., Fradkov, A.L., and Hill, D.D., Passivity and Passification of Nonlinear Systems (Review), Avtom. Telemekh., 2000, no. 3, pp. 3-37.
12. Angeli, D., Sontag, E.D., and Wang, Y., A Characterization of Integral Input to State Stability, Syst. Control Lett., 1999, vol. 38, pp. 209-217.
13. Sontag, E.D. and Wang, Y., Output-to-State Stability and Detectability of Nonlinear Systems, Syst. Control Lett., 1997, vol. 29, pp. 279-290.
14. Sontag, E.D., Smooth Stabilization Implies Coprime Factorization, IEEE Trans. Automat. Control, 1989, vol. 34, pp. 435-443.
15. Sontag, E.D. and Wang, Y., Various Results Concerning Set Input-to-State Stability, Proc. IEEE CDC 95, IEEE Publications, 1995, pp. 1330-1335.
16. Angeli, D., Input-to-state Stability of PD-Controlled Robotic Systems, Automatica, 1999, vol. 35, pp. 1285-1290.
17. Sontag, E.D. and Wang, Y., Notions of Input to Output Stability, Syst. Control Lett., 1999, vol. 38, pp. 235-248.
18. Nemytskiy, V.V., Oscillations in Multidimention Dynamical Systems, Proc. Int. Sympos. on Nonlinear Oscillations, 1963.
19. Sontag, E.D., Asymptotic Amplitudes and Cauchy Gains. A Small Gain Principle and an Application to Inhibitory Biological Feedback, Syst. Control Lett., 2000, vol. 47, pp. 167-179.
20. Fradkov, A.L. and Pogromsky, A.Yu., Introduction to Oscillations and Chaos, Singapore: World Scientific, 1998.
21. Hayachi, C., Nonlinear Oscillations in Physical Systems, New York: McGraw-Hill, 1964.
22. LaSalle, J. and Lefschetz, S., Stability by Liapunov's Direct Method, New York: Academic, 1961. Translated under the title Issledovanie ustoichivosti pryamym metodom Lyapunova, Moscow: Mir, 1964.
23. LaSalle, J. and Lefschetz, S., Stability by Liapunov's Direct Method, New York: Academic, 1961. Translated under the title Issledovanie ustoichivosti pryamym metodom Lyapunova, Moscow: Mir, 1964.
24. Arcak, M. and Teel, A., Input-to-State Stability for a Class of Lurie Systems, Automatica, 2002, vol. 38, pp. 1945-1949.
25. Fomin, V.N., Fradkov, A.L., and Yakybovich, V.A., Adaptivnoe upravlenie dinamicheskimi sistemami (Adaptive Control of Dynamic Systems), Moscow: Nauka, 1981.
26. Sontag, E.D., and Wang, Y., New Characterization of the Input to State Stability Property, IEEE Trans. Automat. Control, 1996, vol. 41, pp. 1283-1294.