Further constructions of control-Lyapunov functions and stabilizing feedbacks for systems satisfying the Jurdjevic-Quinn conditions

IEEE Transactions on Automatic Control

Volumn 51, Issue 2, 2006, Pages 360-365

  Mazenc, Frédéric ^a   Malisoff, Michael ^b  

^a INRIA   (France)

^b LOUISIANA STATE UNIVERSITY   (United States)

Author keywords

Lyapunov functions; Nonlinear; Stabilization

Indexed keywords

ACTUATORS; CONTROL SYSTEM SYNTHESIS; LYAPUNOV METHODS; STABILIZATION; STATE FEEDBACK; SYSTEM STABILITY;

INTEGRAL INPUT-TO-STATE STABLE-TO-ACTUATOR ERRORS; JURDJEVIC-QUINN CONDITIONS; SMOOTH CONTROL LYAPUNOV FUNCTIONS;

NONLINEAR CONTROL SYSTEMS;

EID: 33244461550     PISSN: 00189286     EISSN: None     Source Type: Journal    
DOI: 10.1109/TAC.2005.863500     Document Type: Article

References (19)

1. D. Angeli, "Input to state stability of PD controlled robotic systems," Automatica, vol. 35, no. 7, pp. 1285-1290, Jul. 1999.
2. D. Angeli, E. Sontag, and Y. Wang, "A characterization of integral input-to-state stability," IEEE Trans. Autom. Control, vol. 45, no. 6, pp. 1082-1097, Jun. 2000.
3. M. Arcak, D. Angeli, and E. Sontag, "A unifying integral ISS framework for stability of nonlinear cascades," SIAM J. Control Optim., vol. 40, pp. 1888-1904,2002.
4. L. Faubourg and J.-B. Pomet, "Control Lyapunov functions for homogeneous Jurdjevic-Quinn systems," ESAIM: Control, Optim. Calc. Variat., vol. 5, pp. 293-311, 2000.
5. R. Freeman and P. Kokotovic, Robust Control of Nonlinear Systems. Boston, MA: Birkhäuser, 1996.
6. A. Isidori, Nonlinear Control Systems II. London, U.K.: Springer-Verlag, 1999.
7. M. Jankovic, "Control Lyapunov-Razumikhin functions and robust stabilization of time delay systems," IEEE Trans. Autom. Control, vol. 46, no. 7, pp. 1048-1060, Jul. 2001.
8. V. Jurdjevic and J. Quinn, "Controllability and stability," J. Diff. Equat., vol. 28, pp. 381-389, 1978.
9. J. Kurzweil, "On the inversion of Liapunov's second theorem on stability of motion," A.M.S. Trans. Ser II, vol. 24, pp. 19-77, 1956.
10. W. Liu, Y. Chitour, and E. Sontag, "On finite gain stability of linear systems subject to input saturation," SIAM J. Control Optim., vol. 34, pp. 1190-1219, 1996.
11. F. Mazenc, S. Mondié, and S. Niculescu, "Global stabilization of oscillators with bounded delayed input," Syst. Control Lett., vol. 53, pp. 415-422, 2004.
12. F. Mazenc and D. Nesic, "Strong Lyapunov functions for systems satisfying the conditions of LaSalle," IEEE Trans. Autom. Control, vol. 49, no. 6, pp. 1026-1030, Jun. 2004.
13. L. Praly and Y. Wang, "Stabilization in spite of matched unmodeled dynamics and an equivalent definition of input-to-state stability," Math. Control Signals Syst., vol. 9, pp. 1-33, 1996.
14. R. Sepulchre, M. Jankovic, and P. Kokotovic, Constructive Nonlinear Control. New York: Springer-Verlag, 1996.
15. E. Sontag, "Smooth stabilization implies coprime factorization," IEEE Trans. Autom. Control, vol. 34, no. 4, pp. 435-443, Apr. 1989.
16. E. Sontag, "A universal construction of Artstein's theorem on nonlinear stabilization," Syst. Control Lett., vol. 13, pp. 117-123, 1989.
17. E. Sontag, Mathematical Control Theory, 2nd ed. New York: Springer-Verlag, 1998.
18. A. Teel, "Connections between Razumikhin-type theorems and the ISS nonlinear small gain theorems," IEEE Trans. Autom. Control, vol. 43, no. 7, pp. 960-964, Jul. 1998.
19. 2-Gain and Passivity Techniques in Nonlinear Control. New York: Springer-Verlag, 2000.