Control of nonlinear chained systems: from the Routh-Hurwitz stability criterion to time-varying exponential stabilizers

IEEE Transactions on Automatic Control

Volumn 45, Issue 1, 2000, Pages 141-146

  Morin, P ^a   Samson, C ^a  

^a INRIA   (France)

Author keywords

[No Author keywords available]

Indexed keywords

ASYMPTOTIC STABILITY; CONVERGENCE OF NUMERICAL METHODS; FEEDBACK CONTROL; MATHEMATICAL TRANSFORMATIONS; MATRIX ALGEBRA; POLYNOMIALS; STABILITY CRITERIA; TIME VARYING CONTROL SYSTEMS;

EXPONENTIAL STABILIZERS; NON HOLONOMIC SYSTEM; ROUTH-HURWITZ STABILITY CRITERION; TIME VARYING FEEDBACK;

NONLINEAR CONTROL SYSTEMS;

EID: 0033893932     PISSN: 00189286     EISSN: None     Source Type: Journal    
DOI: 10.1109/9.827372     Document Type: Article

References (19)

1. R. W. Brockett, "Asymptotic stability and feedback stabilization," in Differential Geometric Control Theory, R. W. Brockett, R. S. Millman, and H. H. Sussmann, Eds, 1983.
2. C.-T. Chen, Linear System Theory and Design. New York: Holt, Rinehart, and Winston, Inc., 1984.
3. J.-M. Coron, "Global asymptotic stabilization for controllable systems without drift," Math. Contr. Sign. Syst., vol. 5, pp. 295-312, 1992.
4. _, "On the stabilization in finite time of locally controllable systems by means of continuous time-varying feedback laws," SIAM J. Contr. Optim., vol. 33, pp. 804-833, 1995.
5. H. Hermes, "Nilpotent and high-order approximations of vector fields systems," SIAM Rev., vol. 33, pp. 238-264, 1991.
6. J. P LaSalle, "Stability theory for ordinary differential equations," J. Differential Equations, vol. 4, pp. 57-65, 1968.
7. R. T. M'Closkey and R. M. Murray, "Non-holonomic systems and exponential convergence: Some analysis tools," in Proc. IEEE Conf. Decision Contr., 1993, pp. 943-948.
8. _, "Exponential stabilization of nonlinear driftless control systems viatime-varying homogeneous feedback," in Proc. IEEE Conf. Decision Contr., 1994, pp. 1317-1322.
9. _, "Exponential stabilization of driftless nonlinear control systems using homogeneous feedback," IEEE Trans Automat. Contr., vol. 42, pp. 614-628, 1997.
10. P. Morin and C. Samson, "Application of backstepping techniques to the time-varying exponential stabilization of chained form systems," Eur. J. Contr., vol. 3, pp. 15-36, 1997.
11. _, "Control of nonlinear chained systems; Routh-Hurwitz stability criterion to time-varying exponential stabilizers," INRIA Rep., Available at http://www.inria.fr/rapports/sophia/RR-3126.html.
12. R. M. Murray and S. S. Sastry, "Non-holonomic motion planning: Steering using sinusoids," IEEE Trans Automat. Contr., vol. 38, pp. 700-716, 1993.
13. J.-B. Pomet, "Explicit design of time-varying stabilizing control laws for a class of controllable systems without drift," Syst. Contr. Lett., vol. 18, pp. 467-473, 1992.
14. J.-B. Pomet and C. Samson, "Exponential stabilization of nonholonomic systems in power form," in Proc. IFAC Symp. Robust Contr. Design, 1994, pp. 447-452.
15. C. Samson, "Velocity and torque feedback control of a nonholonomic cart," in Int. Workshop Adaptative Nonlinear Contr.: Issues Robot., Grenoble, France, 1990.
16. _, "Control of chained systems. Application to path following and time-varying point-stabilization," IEEE Trans. Automat. Contr., vol. 40, pp. 64-77, 1995.
17. R. Sepulchre, G. Campion, and V. Wertz, "Some remarks about periodic feedback stabilization," in Proc. IFAC Nonlinear Contr. Syst. in Proc. Design Symp. (NOLCOS), 1992, pp. 418-423.
18. O. J. Sørdalen, "Conversion of the kynematics of a car with n trailers into a chained form," in Proc. IEEE Conf. Robotics Automat., 1993, pp. 382-387.
19. A. R. Teel, R. M. Murray, and G. Walsh, "Non-holonomic control systems From steering to stabilization with sinusoids," in Proc. IEEE Conf. Decision Contr., 1992, pp. 1603-1609.