A small-gain control method for nonlinear cascaded systems with dynamic uncertainties

IEEE Transactions on Automatic Control

Volumn 42, Issue 3, 1997, Pages 292-308

  Jiang, Zhong Ping ^a,b   Mareels, Iven M Y ^a,c  

^a IEEE   (Australia)

^b UNIVERSITY OF SYDNEY   (Australia)

^c UNIVERSITY OF MELBOURNE   (Australia)

Author keywords

Global asymptotic stability; Input to state stability; Nonlinear cascaded systems; Nonlinear gain; Robust control

Indexed keywords

INPUT TO STATE STABILITY; NONLINEAR CASCADED SYSTEMS; NONLINEAR GAIN; SMALL GAIN CONTROL METHOD; STEPWISE CONSTRUCTIVE CONTROL METHODOLOGY;

ASYMPTOTIC STABILITY; CONTROL SYSTEM SYNTHESIS; DYNAMICS; NONLINEAR CONTROL SYSTEMS; ROBUSTNESS (CONTROL SYSTEMS); SYSTEM STABILITY; TIME VARYING CONTROL SYSTEMS;

CASCADE CONTROL SYSTEMS;

EID: 0031102352     PISSN: 00189286     EISSN: None     Source Type: Journal    
DOI: 10.1109/9.557574     Document Type: Article

References (42)

1. B. R. Barmish, M. R. Corless, and G. Leitman, "A new class of stabilizing controllers for uncertain dynamical systems," SIAM J. Contr. Optimiz., vol. 21, no. 2, pp. 246-255, 1983.
2. C. Byrnes and A. Isidori, "New results and examples in nonlinear feedback stabilization," Syst. Contr. Lett., vol. 12, pp. 437-442, 1989.
3. _, "Asymptotic stabilization of minimum phase nonlinear systems," IEEE Trans. Automat. Contr., vol. 36, pp. 1122-1137, 1991.
4. C. Byrnes, A. Isidori, and J. Willems, "Passivity, feedback equivalence and the global stabilization of minimum phase nonlinear systems," IEEE Trans. Automat. Contr., vol. 36, pp. 1228-1240, 1991.
5. Y. H. Chen and G. Leitman, "Robustness of uncertain systems in the absence of matching assumptions," Int. J. Contr., vol. 45, no. 5, pp. 1527-1542, 1987.
6. C. Desoer and M. Vidyasagar, Feedback Systems: Input-Output Properties. New York: Academic, 1975.
7. R. A. Freeman and P. V. Kokotović, " Design of 'softer' robust nonlinear control laws," Automatica, vol. 29, no. 6, pp. 1425-1437, 1993.
8. _, "Global robustness of nonlinear systems to state measurement disturbances," in Proc. 32nd Conf. Decision Contr., San Antonio, TX, Dec. 1993, pp. 1507-1512.
9. J. Imura, T. Sugie, and T. Yoshikawa, "Global robust stabilization of nonlinear cascaded systems," IEEE Trans. Automat. Contr., vol. 39, pp. 1084-1089, 1994.
10. A. Isidori, Nonlinear Control Systems, 2nd ed. New York: Springer-Verlag, 1989.
11. Z. P. Jiang, "Quelques résultats de stabilization robuste. Applications à la commande," Ph. D. dissertation, Ecole des Mines de Paris, 1993.
12. Z. P. Jiang and J.-B. Pomet, "A note on 'Robust control of nonlinear systems with input unmodeled dynamics,'" Rapport de Recherche, I. N. R. I. A., no. 2293, June 1994.
13. Z. P. Jiang and L. Praly, "Preliminary results about robust Lagrange stability in adaptive regulation," Int. J. Adaptive Contr. Signal Processing, vol. 6, pp. 285-307, 1992.
14. _, "Technical results for the study of robustness of Lagrange stability," Syst. Contr. Lett., vol. 23, pp. 67-78, 1994.
15. Z. P. Jiang, A. Teel, and L. Praly, "Small-gain theorem for ISS systems and applications," Math. Contr. Signals Syst., vol. 7, pp. 95-120, 1994.
16. I. Kanellakopoulos, P. V. Kokotović, and A. S. Morse, "Systematic design of adaptive controllers for feedback linearizable systems," IEEE Trans. Automat. Contr., vol. 36, pp. 1241-1253, 1991.
17. _, "A toolkit for nonlinear feedback design," Syst. Contr. Lett., vol. 18, pp. 83-92, 1992.
18. H. K. Khalil, Nonlinear Systems. New York: Macmillan, 1992.
19. P. V. Kokotović and H. J. Sussmann, "A positive real condition for global stabilization of nonlinear systems," Syst. Contr. Lett., vol. 13, pp. 125-133, 1989.
20. M. Krstić, J. Sun, and P. V. Kokotović, "Robust control of nonlinear systems with input unmodeled dynamics," Univ. California, Jan. 1994, Tech. Rep. CCEC 94-0125.
21. M. Krstić and P. V. Kokotović, "On extending the Praly-Jiang-Teel design to systems with nonlinear input unmodeled dynamics," Univ. California, Feb. 1994, Tech. Rep. CCEC 94-0211.
22. Y. Lin, E. D. Sontag, and Y. Wang, "Lyapunov-function characterizations of stability and stabilization for parameterized families of systems," in Proc. 32nd IEEE Conf. Dec. Contr., San Antonio, TX, Dec. 1993, pp. 1978-1983.
23. R. Lozano, B. Brogliato, and I. D. Landau, "Passivity and global stabilization of cascaded nonlinear systems," IEEE Trans. Automat. Contr., vol. 37, pp. 1386-1388, 1992.
24. I. M. Y. Mareels and D. J. Hill, "Monotone stability of nonlinear feedback systems," J. Math. Syst. Estimation Contr., vol. 2, pp. 275-291, 1992.
25. R. Marino and P. Tomei, "Robust stabilization of feedback linearizable time-varying uncertain nonlinear systems," Automatica, vol. 29, pp. 181-189, 1993.
26. R. Ortega, "Passivity properties for the stabilization of cascaded nonlinear systems," Automatica, vol. 27, no. 2, pp. 423-424, 1991.
27. L. Praly and Z.-P. Jiang, "Stabilization by output feedback for systems with ISS inverse dynamics," Syst. Contr. Lett. vol. 21, pp. 19-33, 1993.
28. L. Praly and Y. Wang, "Stabilization in spite of matched unmodeled dynamics and an equivalent definition of input-to-state stability," Math. Contr., Signals Syst., vol. 9, pp. 1-33, 1996.
29. Z. Qu, "Model reference robust control of weakly nonminimum phase systems," in Proc. 32nd IEEE Conf. Dec. Contr., San Antonio, TX, Dec. 1993, pp. 996-1001.
30. Z. Qu and D. M. Dawson, "Robust control of cascaded and individually feedback linearizable nonlinear systems," Automatica, vol. 30, no. 6, pp. 1057-1064, 1994.
31. A. Saberi, P. V. Kokotović, and H. Sussmann, "Global stabilization of partially linear composite systems," SIAM J. Contr. Optimization, vol. 28, pp. 1491-1503, 1990.
32. A. Saberi and P. Sannuti, "Observer-based control of uncertain systems with nonlinear uncertainties," Int. J. Contr., vol. 52, no. 5, pp. 1107-1130, 1990.
33. P. Seibert and P. Suarez, "Global stabilization of nonlinear cascade systems," Syst. Contr. Lett., vol. 14, pp. 347-352, 1990.
34. D. Seto, A. M. Annaswamy, and J. Baillieul, "Adaptive control of nonlinear systems with a triangular structure," IEEE Trans. Automat. Contr., vol. 39, pp. 1411-1428, 1994.
35. D. D. Siljak, Decentralized Control of Complex Systems. Boston: Academic, 1991.
36. E. D. Sontag, "Smooth stabilization implies coprime factorization," IEEE Trans. Automat. Contr., vol. 34, pp. 435-443, 1989.
37. _, "Remarks on stabilization and input-to-state stability," in Proc. 28th. IEEE Conf. Dec. Contr., 1989, pp. 1376-1378.
38. _, "Further facts about input-to-state stabilization," IEEE Trans. Automat. Contr., vol. 35, pp. 473-476, 1990.
39. H. Sussmann and P. V. Kokotović, "The peaking phenomenon and the global stabilization of nonlinear systems," IEEE Trans. Automat. Contr., vol. 36, pp. 424-440, 1991.
40. A. Teel and L. Praly, "Tools for semi-global stabilization by partial state and output feedback," SIAM J. Contr. Optimiz., vol. 33, no. 5, pp. 1443-1488, 1995.
41. _, "On output feedback stabilization for systems with ISS inverse dynamics and uncertainties," in Proc. 32nd Conf. Dec. Contr., San Antonio, TX, Dec. 1993, pp. 1942-1947.
42. J. Tsinias, "Sufficient Lyapunov-like conditions for stabilization," Math. Contr. Signals Syst., vol. 2, pp. 343-357, 1989.