Global stabilization and asymptotic tracking for a class of nonlinear systems by means of time-varying feedback

International Journal of Robust and Nonlinear Control

Volumn 13, Issue 6, 2003, Pages 559-588

  Karafyllis, I ^a   Tsinias, J ^a  

^a NATIONAL TECHNICAL UNIVERSITY OF ATHENS   (Greece)

Author keywords

Asymptotic tracking; Global feedback stabilization; Time varying feedback

Indexed keywords

ASYMPTOTIC STABILITY; FEEDBACK CONTROL; FUNCTIONS; INTEGRAL EQUATIONS; MATHEMATICAL MODELS;

TIME-VARYING FEEDBACK;

NONLINEAR CONTROL SYSTEMS;

EID: 0012244391     PISSN: 10498923     EISSN: None     Source Type: Journal    
DOI: 10.1002/rnc.738     Document Type: Article

References (21)

1. Tsinias J. Backstepping design for time-varying nonlinear systems with unknown parameters. Systems & Control Letters 2000; 39(4):219-227.
2. Tsinias J, Karafyllis I. ISS property for time-varying systems and application to partial-static feedback stabilization and asymptotic tracking. IEEE Transactions on Automatic Control 1999; 44(11):2179-2185.
3. Jiang ZP, Nijmeijer H. Backstepping-based tracking control of non-holonomic chained systems. In Proceedings of the 4th European Control Conference, Brussels, Belgium, Paper 672 (TH-M A2), 1997.
4. Jiang ZP, Nijmeijer H. Tracking control of mobile robots: a case study in backstepping. Automatica 1997; 33(7): 1393-1399.
5. Jiang ZP, Lefeber E, Nijmeijer H. Stabilization and tracking of a nonholonomic mobile robot with saturating actuators. In Proceedings of CONTROLO '98, 3rd Portugese Conference on Automatic Control, vol. 2, Coimbra, Portugal, September 1998; 315-320.
6. Jiang ZP, Nijmeijer H. A recursive technique for tracking control of nonholonomic systems in chained form. IEEE Transactions on Automatic Control 1999; 44(2):265-279.
7. Jiang ZP. Lyapunov design of global state and output feedback trackers for non-holonomic control systems. International Journal of Control 2000; 73(9):744-761.
8. Lefeber E, Robertsson A, Nijmeijer H. Linear controllers for tracking chained-form systems. In Stability and Stabilization of Nonlinear Systems, Aeyels D, Lamnabhi-Lagarrigue F, van der Schaft A (eds), Lecture Notes in Control and Information Sciences, vol. 246. Springer: London, 1999; 183-199.
9. Loria A, Panteley E, Melhem K. UGAS of skew-symmetric systems: application to the nonholonomic integrator. Proceedings of NOLCOS, 2001; 1016-1021.
10. Morin P, Samson C. Application of backstepping techniques to the time-varying exponential stabilization of chained form systems. European Journal of Control 1997; 3:15-36.
11. Morin P, Pomet J-B, Samson C. Design of homogeneous time-varying stabilizing control laws for driftless controllable systems via oscillatory approximation of lie brackets in closed loop. SIAM Journal on Control and Optimization 1999; 38(1):22-49.
12. Morin P, Samson C. Exponential stabilization of nonlinear driftless systems with robustness to unmodeled dynamics. ESAIM: Control, Optimisation and Calculus of Variations 1999; 4:1-35.
13. Morin P, Samson C. Robust point-stabilization of nonlinear affine control systems. In Stability and Stabilization of Nonlinear Systems, Aeyels D, Lamnabhi-Lagarrigue F, van der Schaft A (eds), Lecture Notes in Control and Information Sciences, vol. 246. Springer: London, 1999; 215-237.
14. Morin P, Samson C. Control of nonlinear chained systems: from the Routh-Hurwitz stability criterion to time-varying exponential stabilizers. IEEE Transactions on Automatic Control 2000; 45(1):141-146.
15. Pomet J-P. Explicit design of time-varying stabilizing control laws for a class of controllable systems without drift. Systems & Control Letters 1992; 18(2):147-158.
16. Karafyllis I, Tsinias J. Converse Lyapunov theorems for non-uniform in time global asymptotic stability and stabilization by means of time-varying feedback. Proceedings of NOLCOS, 2001; 801-805.
17. Karafyllis I, Tsinias J. A converse Lyapunov theorem for non-uniform in time global asymptotic stability and its application to feedback stabilization. SIAM Journal Control and Optimization, submitted.
18. Hahn W. Stability of Motion. Springer: Berlin, 1967.
19. Brockett RW. Asymptotic stability and feedback stabilization. In Differential Geometric Control Theory, Brockett RW, Millman RS, Sussmann HJ (eds). Birkhauser: Boston, 1983; 181-191.
20. Sordalen OJ, Egeland O. Exponential stabilization of nonholonomic chained systems. IEEE Transactions on Automatic Control 1995; 40(1):35-49.
21. Laiou M-C, Astolfi A. Discontinuous control of high-order generalized chained systems. Systems & Control Letters 1999; 37:309-322.