Formulas relating script K sign ℒ stability estimates of discrete-time and sampled-data nonlinear systems

Systems and Control Letters

Volumn 38, Issue 1, 1999, Pages 49-60

  Nesic D ^a   Teel, A R ^b   Sontag, E D ^c  

^a UNIVERSITY OF MELBOURNE   (Australia)

^b University of California   (United States)

^c RUTGERS UNIVERSITY   (United States)

Author keywords

Discrete time; Input to state stability; Sampled data; Script K sign functions; Stability

Indexed keywords

EID: 0002128292     PISSN: 01676911     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0167-6911(99)00046-8     Document Type: Article

References (24)

1. D. Aeyels, J. Peuteman, A new asymptotic stability criterion for nonlinear time-variant differential equations, IEEE Trans. Automat. Control 43 (1998) 968-971.
2. D. Aeyels, J. Peuteman, On exponential stability of nonlinear time-variant differential equations, Automatica 35 (1999) 1091-1100.
3. B. Castillo, S. Di Gennaro, S. Monaco, D. Normand-Cyrot, On regulation under sampling, IEEE Trans. Automat. Control 42 (1997) 864-868.
4. T. Chen, B.A. Francis, Input-output stability of sampled-data systems, IEEE Trans. Automat. Control 36 (1991) 50-58.
5. T. Chen, B.A. Francis, Optimal Sampled-Data Control Systems, Springer, London, 1995.
6. B.A. Francis, T.T. Georgiou, Stability theory for linear time-invariant plants with periodic digital controllers, IEEE Trans. Automat. Control 33 (1988) 820-832.
7. S.P. Gordon, On converses to the stability theorems for difference equations, SIAM J. Control 10 (1972) 76-81.
8. W. Hahn, Stability of Motion, Springer, Berlin, 1967.
9. L. Hou, A.N. Michel, H. Ye, Some qualitative properties of sampled-data control systems, IEEE Trans. Automat. Control 42 (1997) 1721-1725.
10. B. Jakubczyk, E.D. Sontag, Controllability of nonlinear discrete-time systems: a Lie-algebraic approach, SIAM J. Control Opt. 28 (1990) 1-33.
11. H.K. Khalil, Nonlinear Systems. Prentice-Hall, Englewood Cliffs, NJ, 1996.
12. V. Lakshmikantham, S. Leela, Differential and Integral Inequalities, Vol. 1, Academic Press, New York, 1969.
13. I.M.Y. Mareels, H.B. Penfold, R.J. Evans, Controlling nonlinear time-varying systems via Euler approximations, Automatica 28 (1992) 681-696.
14. M.S. Mousa, R.K. Miller, A.N. Michel, Stability analysis of hybrid composite dynamical systems: descriptions involving operators and difference equations, IEEE Trans. Automat. Control 31 (1986) 603-615.
15. D. Nešić, A.R. Teel, P.V. Kokotović, On the design of a controller based on the discrete-time approximation of the nonlinear plant model, Systems Control Lett., to appear.
16. J. Peuteman, D. Aeyels, Averaging results and the study of uniform asymptotic stability of homogeneous differential equations that are not fast time varying, 1988, accepted for publication.
17. E. Skafidas, A. Fradkov, R.J. Evans, I.M.Y. Mareels, Trajectory-approximation-based adaptive control for nonlinear systems under matching conditions, Automatica 34 (1998) 287-299.
18. E.D. Sontag, An eigenvalue condition for sampled weak controllability of bilinear systems, Systems Control Lett. 7 (1986) 313-316.
19. E.D. Sontag, Smooth stabilization implies coprime factorization, IEEE Trans. Automat. Control 34 (1989) 435-443.
20. E.D. Sontag, Comments of integral variants of ISS, Systems Control Lett. 34 (1998) 93-100.
21. E.D. Sontag, Mathematical Control Theory, Finite Dimensional Systems, 2nd ed., Springer, New York, 1998.
22. H.J. Stetter, Analysis of Discretization Methods for Ordinary Differential Equations, Springer, New York, 1973.
23. A.M. Stuart, A.R. Humphries, Dynamical Systems and Numerical Analysis, Cambridge University Press, New York, 1996.
24. A.R. Teel, J. Peuteman, D. Aeyels, Global asymptotic stability for the averaged implies semi-global practical asymptotic stability for the actual, Proceedings CDC, Tampa, FL, 1998, pp. 1458-1463.