Stabilization of oscillations through backstepping in high-dimensional systems

IEEE Transactions on Automatic Control

Volumn 50, Issue 5, 2005, Pages 705-710

  Aracil, Javier ^a   Gordillo, Francisco ^a   Ponce, Enrique ^a  

^a UNIVERSIDAD DE SEVILLA   (Spain)

Author keywords

Backsteppmg control; Generalized Hamiltonian systems; Hopf bifurcation; Limit cycle stabilization; Nonlinear oscillations

Indexed keywords

BIFURCATION (MATHEMATICS); CLOSED LOOP CONTROL SYSTEMS; HAMILTONIANS; LYAPUNOV METHODS; MATRIX ALGEBRA; OSCILLATIONS; ROBUSTNESS (CONTROL SYSTEMS); SYSTEM STABILITY;

BACKSTEPPING CONTROL; GENERALIZED HAMILTONIAN SYSTEMS; HOPF BIFURCATION; LIMIT CYCLE STABILIZATION; NONLINEAR OSCILLATIONS;

NONLINEAR CONTROL SYSTEMS;

EID: 20344404206     PISSN: 00189286     EISSN: None     Source Type: Journal    
DOI: 10.1109/TAC.2005.847038     Document Type: Article

References (12)

1. 2-Gain and Passivity Techniques in Nonlinear Control. New York: Springer-Verlag, 1989.
2. R. Goldwyn and K. J. Cox. "Limit cycle construction using Liapunov functions," IEEE Trans. Autom. Control, vol. AC-10, no. 1, pp. 97-99, Jan. 1965.
3. D. Green, "Synthesis of systems with periodic solutions satisfying N(x) = 0," IEEE Trans. Circuits Syst., vol. CAS-31, no. 4, pp. 317-326, Apr. 1984.
4. K. Hirai and K. Maeda, "A method of limit-cycle synthesis and its applications,IEEE Trans. Circuit Theory, vol. 19, pp. 631-633, Jun. 1972.
5. J. Aracil, F. Góomez-Estern, and F. Gordillo, "A family of oscillating generalized Hamiltonian systems," in Proc. 2nd IFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control, Seville, Spain, 2003, pp. 93-98.
6. M. Krstic, I. Kanellakopoulos, and P. Kokotovic, Nonlinear and Adaptive Control Design. New York: Wiley, 1995.
7. J. Aracil, F. Gordillo, and J. Acosta, "Stabilization of oscillations in the inverted pendulum," in Proc. XV IFAC World Congr., 2002.
8. K. Fujimoto and T. Sugie, "Canonical transformation and stabilization of generalized Hamiltonian systems," Syst. Control Lett., vol. 42, no. 3, pp. 217-227, Mar. 2000.
9. R. Marino and P. Tomei, Nonlinear Control Design. Upper Saddle River, NJ: Prentice-Hall, 1995.
10. A. Loria, P. Niklasson, and H. Sira-Ramrez, Passivity-Based Control of Euler-Lagrange Systems. New York: Springer-Verlag, 1998.
11. J. Marsden and M. McCraken, The Hopf Bifurcation and Its Applications. New York: Springer-Verlag, 1976.
12. J. Carr, Applications of Centre Manifold Theory. New York: Springer-Verlag, 1981.