Bifurcation control via state feedback for systems with a single uncontrollable mode

SIAM Journal on Control and Optimization

Volumn 38, Issue 5, 2000, Pages 1428-1452

  Kang, Wei ^a  

^a NAVAL POSTGRADUATE SCHOOL   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BIFURCATION (MATHEMATICS); CONTROL SYSTEM ANALYSIS; FEEDBACK CONTROL; INVARIANCE; STATE FEEDBACK; SYSTEM STABILITY;

PITCHFORK BIFURCATION; SADDLE-NODE BIFURCATION; TRANSCRITICAL BIFURCATION;

NONLINEAR CONTROL SYSTEMS;

EID: 0033707050     PISSN: 03630129     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0363012997325927     Document Type: Article

References (26)

1. E. H. ABED AND J.-H. FU, Local feedback stabilization and bifurcation control, I-II. Stationary bifurcation, Systems Control Lett., 8 (1987), pp. 467-473.
2. S. BEHTASH AND S. SASTRY, Stabilization of nonlinear systems with uncontrollable linearization, IEEE Trans. Automat. Control, 33 (1988), pp. 585-591.
3. J. CARR, Application of Center Manifold Theory, Springer-Verlag, New York, 1981.
4. G. CHEN, Control and Synchronization of Chaotic Systems (a Bibliography), ECE Dept., University of Houston, TX. Available via ftp from ftp.egr.uh.edu/pub/TeX/chaos.tex.
5. G. CHEN AND J. L. MOIOLA, An overview of bifurcation, chaos and nonlinear dynamics in control systems, J. Franklin Inst. B, 331 (1994), pp. 819-858.
6. K. M. EVEKER AND C. N. NETT, Control of compression system surge and rotating stall: A laboratory-based "hands-on" introduction, Proceedings of the American Control Conference, Baltimore, MD, International Federation of Automatic Control, 1994, pp. 1307-1311.
7. O. E. FITCH, The Control of Bifurcations with Engineering Applications, Ph.D. Dissertation, Naval Postgraduate School, Monterey, CA, 1997.
8. R. GENESIO, A. TESI, H. O. WANG, AND E. H. ABED, Control of period doubling bifurcations using harmonic balance, Proceedings of the IEEE Conference on Decision and Control, San Antonio, Texas, 1993, pp. 492-497.
9. P. GLENDINNING, Stability, Instability and Chaos: An Introduction to the Theory of Nonlinear Differential Equations, Cambridge University Press, Cambridge, UK, 1994.
10. J. HALE AND H. KOÇAK, Dynamics and Bifurcations, Springer-Verlag, New York, 1991.
11. G. GU, X. CHEN, A. SPARKS, AND S. BANDA, Bifurcation Stabilization with Local Output Feedback, Department of ECE, Louisiana State University, Baton Rouge, LA, preprint.
12. W. KANG AND A. J. KRENER, Extended quadratic controller normal form and dynamic state feedback linearization of nonlinear systems, SIAM J. Control Optim., 30 (1992), pp. 1319-1337.
13. W. KANG, Extended Controller Normal Form, Invariants and Dynamic Feedback Linearization of Nonlinear Control Systems, Ph.D. Dissertation, University of California at Davis, 1991.
14. W. KANG, Bifurcation and normal form of nonlinear control systems - part I, SIAM J. Control Optim., 36 (1998), pp. 193-212.
15. W. KANG, Bifurcation and normal form of nonlinear control systems - part II, SIAM J. Control Optim., 36 (1988), pp. 213-232.
16. W. KANG, Bifurcation and topology of equilibrium sets, Proceedings of the IEEE Conference on Decision and Control, Kobe, Japan, 1996, pp. 2151-2155.
17. W. KANG AND F. PAPOULIAS, Bifurcation and normal forms of dive plane reversal of submersible vehicles, Proceedings of the International Offshore and Polar Engineering Conference, Honolulu, Hawaii, International Society of Offshore and Polar Engineers, 1997, pp. 62-68.
18. A. J. KRENER, The Feedbacks which Soften the Primary Bifurcation of MG 3, Department of Mathematics, University of California at Davis, Davis, CA, preprint.
19. M. KRSTIC, J. M. PROTZ, J. D. PADUANO, AND P. V. KOKOTOVIC, Backstepping designs for jet engine stall and surge control, Proceedings of the IEEE Conference on Decision and Control, New Orleans, LA, 1995, pp. 3049-3055.
20. D.-C. LIAW AND E. H. ABED, Stability analysis and control of rotating stall, Proceedings of the International Federation of Automatic Control Nonlinear Control Systems Design Symposium, Bordeaux, France, 1992.
21. M. A. PINSKY AND B. ESSARY, Normal forms, averaging and resonance control of flexible structures, J. Dynam. Systems, Measurement and Control, 116, N3 (1994), pp. 357-366.
22. M. A. PINSKY AND I. SHUMYATSKY, Feedback stabilization of bifurcation phenomena and its application to the control of voltage instabilities and collapse, in Proceedings of the International Federation of Automatic Control Nonlinear Control Systems Design Symposium, Lake Tahoe, CA, 1995, pp. 58-63.
23. F. E. MCCAUGHAN, Bifurcation analysis of axial flow compressor stability, SIAM J. Appl. Math., 50 (1990), pp. 1232-1253.
24. F. K. MOORE AND E. M. GREITZER, A theory of post-stall transients in axial compression systems - part I: Development of equations, ASME J. Engineering for Gas Turbines and Power, 108 (1986), pp. 68-76.
25. H. O. WANG AND E. H. ABED, Bifurcation control of a chaotic system, Automatica J. IFAC, 31 (1995), pp. 1213-1226.
26. S. WIGGINS, Introduction to Applied Nonlinear Dynamical Systems and Chaos, Springer-Verlag, New York, 1990.