A system-theoretic framework for a wide class of systems II: Input-to-output stability

Journal of Mathematical Analysis and Applications

Volumn 328, Issue 1, 2007, Pages 466-486

  Karafyllis, Iasson ^a  

^a UNIVERSITY OF ATHENS   (Greece)

Author keywords

Hybrid systems; Input to output stability

Indexed keywords

EID: 33845877487     PISSN: 0022247X     EISSN: 10960813     Source Type: Journal    
DOI: 10.1016/j.jmaa.2006.05.060     Document Type: Article

References (32)

1. Clarke F.H., Ledyaev Y.S., Sontag E.D., and Subbotin A.I. Asymptotic controllability implies feedback stabilization. IEEE Trans. Automat. Control 42 10 (1997) 1394-1407
2. Grune L. Stabilization by sampled and discrete feedback with positive sampling rate. In: Aeyels D., Lamnabhi-Lagarrigue F., and van der Schaft A. (Eds). Stability and Stabilization of Nonlinear Systems (1999), Springer-Verlag, London 165-182
3. Grune L. Asymptotic Behavior of Dynamical and Control Systems under Perturbation and Discretization (2002), Springer-Verlag
4. Hale J.K., and Lunel S.M.V. Introduction to Functional Differential Equations (1993), Springer-Verlag, New York
5. Hu B., and Michel A.N. Stability analysis of digital control systems with time-varying sampling periods. Automatica 36 (2000) 897-905
6. Hu B., and Michel A.N. Robustness analysis of digital control systems with time-varying sampling periods. J. Franklin Inst. 337 (2000) 117-130
7. B. Ingalls, Y. Wang, On input-to-output stability for systems not uniformly bounded, Proceedings of NOLCOS 2001
8. Z.P. Jiang, E.D. Sontag, Y. Wang, Input-to-state stability for discrete-time non-linear systems, in: Proc. 14th IFAC World Congress, vol. E, Beijing, 1999, pp. 277-282
9. Jiang Z.P., and Wang Y. Input-to-state stability for discrete-time non-linear systems. Automatica 37 6 (2001) 857-869
10. Jiang Z.P., and Wang Y. A converse Lyapunov theorem for discrete-time systems with disturbances. Systems Control Lett. 45 1 (2002) 49-58
11. Kalman R.E. Mathematical description of linear dynamical systems. J. SIAM Control 1 2 (1963) 152-192
12. Karafyllis I., and Tsinias J. A converse Lyapunov theorem for non-uniform in time global asymptotic stability and its application to feedback stabilization. SIAM J. Control Optim. 42 3 (2003) 936-965
13. Karafyllis I., and Tsinias J. Non-uniform in time ISS and the Small-Gain Theorem. IEEE Trans. Automat. Control 49 2 (2004) 196-216
14. Karafyllis I. The non-uniform in time Small-Gain Theorem for a wide class of control systems with outputs. Eur. J. Control 10 4 (2004) 307-323
15. Karafyllis I. Non-uniform in time robust global asymptotic output stability for discrete-time systems. Int. J. Robust and Nonlinear Control 16 4 (2006) 191-214
16. I. Karafyllis, A system-theoretic framework for a wide class of systems I: Applications to numerical analysis, J. Math. Anal. Appl. (2006), in press
17. Khalil H.K. Nonlinear Systems. second ed. (1996), Prentice Hall
18. Y. Lin, Y. Wang, D. Cheng, On non-uniform and semi-uniform input-to-state stability for time-varying systems, in: Proceedings of the 16th IFAC World Congress, Prague, 2005
19. Malisoff M., Rifford L., and Sontag E.D. Global asymptotic controllability implies input-to-state stabilization. SIAM J. Control Optim. 42 (2004) 2211-2238
20. Marchand N., and Alamir M. Asymptotic controllability implies continuous-discrete time feedback stabilization. Nonlinear Control in the Year 2000 vol. 2 (2000), Springer-Verlag 63-79
21. Pepe P. The Lyapunov's second method for continuous time difference equations. Int. J. Robust Nonlinear Control 13 (2003) 1389-1405
22. Praly L., and Wang Y. Stabilization in spite of matched unmodeled dynamics and an equivalent definition of input-to-state stability. Math. Control Signals Systems 9 (1996) 1-33
23. Savkin A.V., and Evans R.J. Hybrid Dynamical Systems (2002), Birkhäuser, Boston
24. Shim H., and Teel A.R. Asymptotic controllability and observability imply semiglobal practical asymptotic stabilizability by sampled-data output feedback. Automatica (2003) 441-454
25. Sontag E.D. Smooth stabilization implies coprime factorization. IEEE Trans. Automat. Control 34 (1989) 435-443
26. Sontag E.D., and Wang Y. On characterizations of the input-to-state stability property. Systems Control Lett. 24 (1995) 351-359
27. Sontag E.D., and Wang Y. New characterizations of the input-to-state stability. IEEE Trans. Automat. Control 41 (1996) 1283-1294
28. Sontag E.D. Mathematical Control Theory. second ed. (1998), Springer-Verlag, New York
29. Sontag E.D. Comments on integral variants of ISS. Systems Control Lett. 34 (1998) 93-100
30. Sontag E.D. Clocks and insensitivity to small measurement errors. ESAIM Control Optim. Calc. Var. 4 (1999) 537-557
31. Sontag E.D., and Wang Y. Notions of input-to-output stability. Systems Control Lett. 38 (1999) 235-248
32. Sontag E.D., and Wang Y. Lyapunov characterizations of input-to-output stability. SIAM J. Control Optim. 39 (2001) 226-249