Stabilization of nonaffine systems: A constructive method for polynomial systems

IEEE Transactions on Automatic Control

Volumn 50, Issue 4, 2005, Pages 520-526

  Moulay, Emmanuel ^a,b   Perruquetti, Wilfrid ^b  

^a UNIVERSITÉ LILLE 1   (France)

^b ECOLE CENTRALE DE LILLE   (France)

Author keywords

Control Lyapunov function; Nonaffine systems; Polynomial systems; Stabilization

Indexed keywords

COMPUTER SIMULATION; CONTROL THEORY; FEEDBACK CONTROL; LYAPUNOV METHODS; ORDINARY DIFFERENTIAL EQUATIONS; POLYNOMIALS; SYSTEM STABILITY; THEOREM PROVING;

CONTROL LYAPUNOV FUNCTION; DISCONTINUOUS CONTROL; NONAFFINE SYSTEMS; POLYNOMIAL SYSTEMS;

NONLINEAR SYSTEMS;

EID: 17644411681     PISSN: 00189286     EISSN: None     Source Type: Journal    
DOI: 10.1109/TAC.2005.844899     Document Type: Article

References (10)

1. Z. Artstein, "Stabilization with relaxed controls," Nonlinear Anal., Theory, Meth., Appl., vol. 7, no. 11, pp. 1163-1173, 1983.
2. E. Sontag, "A universal construction of Arststein's theorem on nonlinear stabilization," Syst. Control Lett., vol. 13, pp. 117-123, 1989.
3. E. Mickael, "Continuous selections," Ann. Math., vol. 63, no. 2, pp. 361-382, Mar. 1956.
4. J.P. Aubin and A. Cellina, Differential Inclusion. New York: Springer-Verlag, 1984, vol. 264.
5. A. Schinzel, Selected Topics on Polynomials. Ann Arbor, MI: Univ. Michigan Press, 1982.
6. K.K. Hassan, Nonlinear Systems. Upper Saddle River, NJ: Prentice-Hall, 1996.
7. A. F. Filippov, Differential Equations with Discontinuous Righthand Sides, F. M. Arscott, Ed. Boston, MA: Kluwer, 1988.
8. D. Shevitz and B. Paden, "Lyapunov stability of nonsmooth system," IEEE Trans. Autom. Control, vol. 39, no. 9, pp. 1910-1914, Sep. 1994.
9. O. Bethoux, T. Floquet, and J. P. Barbot, "Advanced sliding mode stabilization of a levitation system," presented at the Eur. Control Conf., Cambridge, U.K., 2003.
10. G. V. Smirnov, Introduction to the Theory of Differential Inclusions Providence, RI: AMS, 2002, vol. 41, Graduate Studies in Mathematics.