Input-to-state stability for discrete-time nonlinear systems

Automatica

Volumn 37, Issue 6, 2001, Pages 857-869

  Jiang, Zhong Ping ^a   Wang, Yuan ^b  

^a POLYTECHNIC UNIVERSITY   (United States)

^b FLORIDA ATLANTIC UNIVERSITY   (United States)

Author keywords

Discrete time systems; Input to state stability; Lyapunov functions; Nonlinear small gain; Nonlinear stability

Indexed keywords

CONTROL SYSTEM ANALYSIS; CONTROL SYSTEM SYNTHESIS; DISCRETE TIME CONTROL SYSTEMS; LYAPUNOV METHODS; SYSTEM STABILITY; THEOREM PROVING;

DISCRETE-TIME NONLINEAR SYSTEMS; INPUT-TO-STATE STABILITY;

NONLINEAR CONTROL SYSTEMS;

EID: 0035370502     PISSN: 00051098     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0005-1098(01)00028-0     Document Type: Article

References (30)

1. Agarwal R.P. Difference equations and inequalities. : theory, methods and applications:1992;Marcel Dekker, New York.
2. Byrnes C.I., Lin W. Losslessness, feedback equivalence and the global stabilization of discrete-time nonlinear systems. IEEE Transactions on Automatic Control. 39:1994;83-98.
3. Chen F.-C., Khalil H.K. Adaptive control of a class of nonlinear discrete-time systems using neural networks. IEEE Transactions on Automatic Control. 40:1995;791-801.
4. Coron J.-M., Praly L., Teel A. Feedback stabilization of nonlinear systems. : Sufficient conditions and Lyapunov and input-output techniques Isidori A. Trends in control. 1994;Springer, London.
5. Desoer C., Vidyasagar M. Feedback systems. : Input-output properties:1975;Academic Press, New York.
6. Guo L. On critical stability of discrete-time adaptive nonlinear control. IEEE Transactions on Automatic Control. 42(11):1997;1488-1499.
7. Isidori A. Nonlinear control systems II. 1999;Springer, London.
8. Jiang, Z. P., Lin, Y., & Wang, Y. (2000). A local nonlinear small-gain theorem for discrete-time feedback systems and its applications. Proceedings of the third Asian control conference (ASCC' 2000), Shanghai (pp. 1227-1232).
9. Jiang Z.P., Mareels I.M.Y. A small-gain control method for cascaded nonlinear systems with dynamic uncertainties. IEEE Transactions on Automatic Control. 42:1997;292-308.
10. Jiang Z.P., Mareels I.M.Y., Wang Y. A Lyapunov formulation of the nonlinear small gain theorem for interconnected ISS systems. Automatica. 32:1996;1211-1215.
11. Jiang Z.P., Teel A., Praly L. Small-gain theorem for ISS systems and applications. Mathematics of Control, Signals and Systems. 7:1994;95-120.
12. Jiang, Z. P., & Wang, Y. (2001). A converse Lyapunov theorem for discrete time systems with disturbances. Submitted for publication.
13. Kazakos D., Tsinias J. The input to state stability conditions and global stabilization of discrete-time systems. IEEE Transactions on Automatic Control. 39:1994;2111-3113.
14. Kotsios, St., & Kalouptsisis, N. (1996). Adaptive control for a certain class of nonlinear systems. preprint.
15. Krstić M., Li Z. Inverse optimal design of input-to-state stabilizing nonlinear controllers. IEEE Transactions on Automatic Control. 43:1998;336-350.
16. Krstić M., Kanellakopoulos I., Kokotović P.V. Nonlinear and adaptive control design. 1995;Wiley, New York.
17. Lakshmikantham V., Trigiante D. Theory of difference equations. : Numerical methods and applications:1988;Academic Press, New York.
18. LaSalle J.P. The stability and control of discrete process. 1986;Springer, New York.
19. Lin Y., Sontag E.D., Wang Y. A smooth converse Lyapunov theorem for robust stability. SIAM Journal on Control and Optimization. 34:1996;124-160.
20. Mareels I.M.Y., Hill D.J. Monotone stability of nonlinear feedback systems. Journal of Mathematical Systems and Estimation Control. 2:1992;275-291.
21. Nijmeijer H., van der Schaft A. Nonlinear dynamical control systems. 1990;Springer, New York.
22. Praly L., Jiang Z.P. Stabilization by output feedback for systems with ISS inverse dynamics. Systems & Control Letters. 21:1993;19-33.
23. Praly L., Wang Y. Stabilization in spite of matched unmodeled dynamics and an equivalent definition of input-to-state stability. Mathematics of Control, Signals and Systems. 9:1994;1-33.
24. Sontag E.D. Smooth stabilization implies coprime factorization. IEEE Transactions on Automatic Control. 34:1989;435-443.
25. Sontag E.D. Further facts about input to state stabilization. IEEE Transactions on Automatic Control. 35:1990;473-476.
26. Sontag E.D., Wang Y. On characterizations of the input to state stability property. Systems & Control Letters. 24:1995;351-359.
27. Sontag E.D., Wang Y. New characterizations of the input to state stability property. IEEE Transactions on Automatic Control. 41:1996;1283-1294.
28. Teel A.R. A nonlinear small-gain theorem for the analysis of control systems with saturation. IEEE Transactions on Automatic Control. 41:1996;1256-1270.
29. Tsinias J.T. Versions of Sontag's "input to state stability condition" and the global stabilization problem. SIAM Journal on Control and Optimization. 31:1993;928-941.
30. Tsinias, J., Kotsios, S., & Kalouptsidis, N. (1990). Topological dynamics of discrete-time systems. Robust control of linear systems and nonlinear control, Proceedings of international symposium MTNS-89, vol. II (pp. 457-463). Boston: Birkhauser.