Growth rate conditions for uniform asymptotic stability of cascaded time-varying systems

Automatica

Volumn 37, Issue 3, 2001, Pages 453-460

  Panteley, Elena ^a   Loría, Antonio ^b  

^a INSTITUTE OF PROBLEMS OF MECHANICAL ENGINEERING   (Russian Federation)

^b CNRS   (France)

Author keywords

[No Author keywords available]

Indexed keywords

ASYMPTOTIC STABILITY; CONTROL SYSTEM ANALYSIS; SYSTEM STABILITY; TIME VARYING CONTROL SYSTEMS;

NON AUTONOMOUS SYSTEMS; TRACKING CONTROL;

CASCADE CONTROL SYSTEMS;

EID: 0035284097     PISSN: 00051098     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0005-1098(00)00169-2     Document Type: Article

References (24)

1. Janković M., Sepulchre R., Kokotović P.V. Constructive Lyapunov stabilization of non linear cascaded systems. IEEE Transactions on Automatic Control. 41:1996;1723-1736.
2. Jiang Z.P., Mareels I. A small gain control method for nonlinear cascaded systems with dynamic uncertainties. IEEE Transactions on Automatic Control. 42(3):1997;1-17.
3. Kanellakopoulos I., Krstić M., Kokotović P. Nonlinear and adaptive control design. 1995;Wiley, New York.
4. Khalil H. Nonlinear systems. 2nd ed. 1996;Macmillan, New York.
5. Kurzweil J. On the inversion of Ljapunov's second theorem on stability of motion. American Mathematic Society Translations. 24:1956;19-77.
6. Lefeber, A. A. J. (2000). Tracking control of nonlinear mechanical systems. Ph. D. thesis, University of Twente, Enschede, Netherlands.
7. Lin Y., Sontag E.D., Wang Y. A smooth converse Lyapunov theorem for robust stability. SIAM Journal on Control and Optimisation. 34:1996;124-160.
8. Loría, A., Nijmeijer, H., & Egeland, O. (1998). Controlled synchronization of two pendula: Cascaded structure approach. In Proceedings of the American control conference, Philadelphia, PA.
9. Mazenc F., Praly L. Adding integrators, saturated controls and global asymptotic stabilization of feedforward systems. IEEE Transactions on Automatic Control. 41:1996;1559-1579.
10. Mazenc, F., & Praly, L. (1997). Asymptotic tracking of a state reference for systems with a feedforward structure. In Proceedings of the fourth European control conference, Brussels, Belgium, paper no. 954. Automatica, in preparation.
11. Panteley, E., & Loría, A. (1997). Global uniform asymptotic stability of cascaded nonautonomous nonlinear systems. In Proceedings of the fourth European control conference, Louvain-La-Neuve, Belgium, Julis. Paper no. 259.
12. Panteley E., Loría A. On global uniform asymptotic stability of non linear time-varying non autonomous systems in cascade. Systems and Control Letters. 33(2):1998;131-138.
13. Panteley, E., & Loría, A. (1999). Growth rate conditions for stability of cascaded time-varying systems and their applications. Technical report 99-158, Lab. d'Automatique de Grenoble, UMR CNRS 5528.
14. Panteley E., Loría A., Sokolov A. Global uniform asymptotic stability of nonlinear nonautonomous systems: application to a turbo-diesel engine. European Journal of Control. 5:1999;107-115.
15. Panteley E., Ortega R. Cascaded control of feedback interconnected systems: application to robots with AC drives. Automatica. 33(11):1997;1935-1947.
16. Praly L., Wang Y. Stabilization in spite of matched unmodelled dynamics and an equivalent definition of input-to-state-stability. Mathematics of Control Signals and Systems. 9:1996;1-33.
17. Rouche N., Mawhin J. Ordinary differential equations II: Stability and periodical solutions. 1980;Pitman, London.
18. Saberi A., Kokotović P.V., Sussmann H.J. Global stabilization of partially linear systems. SIAM Journal of Control and Optimization. 28:1990;1491-1503.
19. Sansone G., Conti R. Nonlinear Differential equations. 1964;Pergamon, Oxford.
20. Seibert P., Suárez R. Global stabilization of nonlinear cascaded systems. Systems and Control Letters. 14:1990;347-352.
21. Sontag E. Smooth stabilization implies coprime factorization. IEEE Transactions on Automatic Control. 34(4):1989;435-443.
22. Sontag, E. D. (1989b). Remarks on stabilization and input-to-state stability. In Proceedings of the 28th IEEE Conference on decision control, Tampa, Fl (pp. 1376-1378).
23. Teel, A. (1998). Lyapunov function theorems: statements and constructions. Notes from advanced nonlinear systems theory. Course no. ECE 594D, University of California, Santa Barbara, CA, USA.
24. Yoshizawa, T. (1966). Stability theory by Lyapunov's second method. The Mathematical Society of Japan, Tokyo.