Nonlinear small-gain condition covering iISS systems: Necessity and sufficiency from a Lyapunov perspective

Proceedings of the IEEE Conference on Decision and Control

Volumn , Issue , 2006, Pages 355-360

  Ito, Hiroshi ^a   Jiang, Zhong Ping ^b  

^a KYUSHU INSTITUTE OF TECHNOLOGY   (Japan)

^b POLYTECHNIC UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

FUNCTION EVALUATION; LARGE SCALE SYSTEMS; LYAPUNOV FUNCTIONS;

INPUT-TO-STATE STABLE (ISS) SUBSYSTEMS; UNIVERSAL REPRESENTATION;

NONLINEAR SYSTEMS;

EID: 39649097615     PISSN: 07431546     EISSN: 25762370     Source Type: Conference Proceeding    
DOI: 10.1109/cdc.2006.377605     Document Type: Conference Paper

References (16)

1. D. Angeli and A. Astolfi, "A tight small gain theorem for not necessarily ISS systems," in Proc. 44th IEEE Conf. Decision Contr., 2005, pp. 5427-5431.
2. D. Angeli, E. Sontag and Y. Wang, "A characterization of integral input-to-state stability," IEEE Trans. Automat. Control, vol. 45, pp. 1082-1097, 2000.
3. R. Freeman, "On the necessity of the small-gain theorem in the performance analysis of nonlinear systems," in Proc. IEEE Conf. Decision Contr., 2000, pp. 51-56.
4. J. Gonçalves and M. Dahleh, "Necessary conditions for robust stability of a class of nonlinear systems," Automatica,vol.34, pp.705-714, 1998.
5. A. Isidori, Nonlinear control systems II. New York: Springer, 1999.
6. H. Ito, "Stability criteria for interconnected iISS systems and ISS systems using scaling of supply rates," in Proc. 2004 American Control Conference, 2004, pp. 1055-1060.
7. H. Ito, "Explicit solutions to state-dependent scaling problems for interconnected iISS and ISS nonlinear systems," in Proc. 2005 American Control Conference, 2005, pp. 4131-4136.
8. H. Ito, "State-dependent scaling problems and stability of interconnected iISS and ISS systems," IEEE Trans. Automat. Control, to appear in 2006.
9. H. Ito and Z.P. Jiang, "On necessary conditions for stability of interconnected iISS systems," in Proc. 2006 American Control Conference, 2006, pp. 1499-1504.
10. Z.P. Jiang, I. Mareels, and Y. Wang, "A Lyapunov formulation of the nonlinear small-gain theorem for interconnected ISS systems," Automatica, vol. 32, pp. 1211-1215, 1996.
11. Z.P. Jiang, A. Teel, and L. Praly, "Small-gain theorem for ISS systems and applications," Mathe.Contr.Signals and Syst.,vol.7,pp.9- 120,1994.
12. J. Shamma and R. Zhao, "Fading-memory feedback systems and robust stability", Automatica, vol. 29, pp. 191-200, 1993.
13. E. Sontag, "Smooth stabilization implies coprime factorization," IEEE Trans. Automat. Control, vol. 34, pp. 435-443, 1989.
14. E. Sontag, "Comments on integral variants of ISS," Systems and Control Letters, vol. 34, pp. 93-100, 1998.
15. E. Sontag and Y. Wang, "On characterizations of input-to-state stability property," Syst. Contr. Lett., vol. 24, pp. 351-359, 1995.
16. A. Teel, "A nonlinear small gain theorem for the analysis of control systems with saturation," IEEE Trans. Automat. Control, vol. 41, pp. 1256-1270, 1996.