Bifurcation and normal form of nonlinear control systems, part I

SIAM Journal on Control and Optimization

Volumn 36, Issue 1, 1998, Pages 193-212

  Kang, Wei ^a  

^a NAVAL POSTGRADUATE SCHOOL   (United States)

Author keywords

Bifurcations; Invariants; Linearly controllable; Nonlinear systems; Normal forms; Stabilizable

Indexed keywords

BIFURCATION (MATHEMATICS); INVARIANCE; LINEAR CONTROL SYSTEMS; SYSTEM STABILITY;

NORMAL FORMS;

NONLINEAR CONTROL SYSTEMS;

EID: 0031676701     PISSN: 03630129     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0363012995290288     Document Type: Article

References (16)

1. E. ABED AND J.-H. FU, Local feedback stabilization and bifurcation control, I. Hopf bifurcation, Systems Control Lett., 7 (1986), pp. 11-17.
2. E. ABED AND J.-H. FU, Local feedback stabilization and bifurcation control, II. Stationary bifurcation., Systems Control Lett., 8 (1987), pp. 467-473.
3. V. I. ARNOLD, Geometrical Methods in the Theory of Ordinary Differential Equations, 2nd ed., Springer-Verlag, Berlin, New York, 1988.
4. J. CARR, Application of Center Manifold Theory, Springer-Verlag, New York, 1981.
5. F. COLONIUS AND W. KLIEMANN, Controllability and stabilization of one-dimensional systems near bifurcation points, Systems Control Lett., 24 (1995), pp. 87-95.
6. J. HALE AND H. KOCAK, Dynamics and Bifurcations, Springer-Verlag, Berlin, New York, 1991.
7. T. KAILATH, Linear Systems, Prentice-Hall, Inc., Englewood Cliffs, NJ, 1980.
8. W. KANG AND A. J. KRENER, Extended quadratic controller normal form and dynamic feedback linearization of nonlinear systems, SIAM J. Control Optim., 30 (1992), pp. 1319-1337.
9. W. KANG, Quadratic normal forms of nonlinear control systems with uncontrollable linearization, in Proc. IEEE Conf. on Decision and Control, New Orleans, 1995, pp. 608-612.
10. W. KANG, Extended controller form and invariants of nonlinear control systems with a single input, J. Math. Systems Estim. Control, 4 (1994), pp. 253-256.
11. M. KRSTIC, J. M. PROTZ, J. D. PADUANO, AND P. V. KOKOTOVIC, Backstepping designs for jet engine stall and surge control, Proc. IEEE Conf. Decision and Control, New Orleans, 1995, pp. 3049-3055.
12. D.-C. LIAW AND E. H. ABED, Stability analysis and control of rotating stall, in Proc. IFAC Nonlinear Control Systems Design Symposium, Bordeaux, France, June 1992.
13. F. E. MCCAUGHAN, Bifurcation analysis of axial flow compressor stability, SIAM J. Appl. Math., 50 (1990), pp. 1232-1253.
14. H. NIJMEIJER AND A. J. VAN DER SCHAFT, Nonlinear Dynamical Control Systems, Springer-Verlag, New York, 1990.
15. S. WIGGINS, Introduction to Applied Nonlinear Dynamical Systems and Chaos, Springer-Verlag, 1990.
16. W. KANG, Bifurcation and normal form of nonlinear control systems, Part II, SIAM J. Control Optim., 36 (1998), pp. 213-232.