Asymptotic behaviour of nonlinear systems

American Mathematical Monthly

Volumn 111, Issue 10, 2004, Pages 864-889

  Logemann, Hartmut ^a   Ryan, Eugene P ^a  

^a University of Bath   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 10844247079     PISSN: 00029890     EISSN: None     Source Type: Journal    
DOI: 10.2307/4145095     Document Type: Review

References (33)

1. H. Amann, Ordinary Differential Equations: An Introduction to Nonlinear Analysis, Walter de Gruyter, Berlin, 1990.
2. J. P. Aubin and A. Cellina, Differential Inclusions, Springer-Verlag, Berlin, 1984.
3. I. Barbälat, Systèmes d'équations différentielles d'oscillations non linéaires, Revue de Mathématiques Pures et Appliquées IV (1959) 267-270.
4. G. D. Birkhoff, Dynamical Systems, Colloquium Publications, no. 9, American Mathematical Society, Providence, 1927.
5. C. I. Byrnes and C. F. Martin, An integral-invariance principle for nonlinear systems, IEEE Trans. Automatic Control AC-40 (1995) 983-994.
6. F. H. Clarke, Optimization and Nonsmooth Analysis, Wiley, New York, 1983.
7. F. H. Clarke, Yu. S. Ledyaev, R. J. Stern, and P. R. Wolenski, Nonsmooth Analysis and Control Theory, Springer-Verlag, New York, 1998.
8. E. A. Coddington and N. Levinson, Theory of Ordinary Differential Equations, McGraw-Hill, New York, 1955.
9. C. Corduneanu, Integral Equations and Stability of Feedback Systems, Academic Press, New York, 1973.
10. K. Deimling, Multivalued Differential Equations, Walter de Gruyter, Berlin, 1992.
11. W. Desch, H. Logemann, E. P. Ryan, and E. D. Sontag, Meagre functions and asymptotic behaviour of dynamical systems, Nonlinear Analysis: Theory, Methods & Applications 44 (2001) 1087-1109.
12. A. F. Filippov, Differential Equations with Discontinuous Righthand Sides, Kluwer, Dordrecht, 1988.
13. W. Hahn, Stability of Motion, Springer-Verlag, Berlin, 1967.
14. P. R. Halmos, Measure Theory, Springer-Verlag, New York, 1974.
15. R. E. Kalman and J. E. Bertram, Control systems analysis and design via the "second method" of Lyapunov; part I: continuous-time systems, Trans. ASME 82 (1960) 371-393.
16. H. W. Knobloch and F. Kappel, Gewöhnliche Differentialgleichungen, B. G. Teubner, Stuttgart, 1974.
17. J. P. LaSalle, The extent of asymptotic stability, Proc. Nat. Acad. Sci. USA 46 (1960) 363-365.
18. _, Some extensions of Liapunov's Second Method, IRE Trans. Circuit Theory CT-7 (1960) 520-527.
19. _, Stability theory for ordinary differential equations, J. Differential Equations 4 (1968) 57-65.
20. _, The Stability of Dynamical Systems, SIAM, Philadelphia, 1976.
21. E. H. Lieb and M. Loss, Analysis, American Mathematical Society, Providence, 1997.
22. H. Logemann and E. P. Ryan, Non-autonomous systems: Asymptotic behaviour and weak invariance principles, J. Differential Equations 189 (2003) 440-460.
23. A. M. Lyapunov, Problème général de la stabilité du mouvement, Ann. Fac. Sci. Toulouse 9 (1907) 203-474; reprinted in Ann. Math. Study, no. 17, Princeton University Press, Princeton, 1949.
24. A. M. Lyapunov, Problème général de la stabilité du mouvement, Ann. Fac. Sci. Toulouse 9 (1907) 203-474; reprinted in Ann. Math. Study, no. 17, Princeton University Press, Princeton, 1949.
25. A. M. Lyapunov. The general problem of the stability of motion (trans. A. T. Fuller), Int. J. Control 55 (1992) 531-773.
26. V. M. Popov, Hyperstability of Control Systems, Springer-Verlag, Berlin, 1973.
27. E. P. Ryan. Discontinuous feedback and universal adaptive stabilization, in Control of Uncertain Systems, D. Hinrichsen and B. Mårtensson, eds., Birkhäuser, Boston, 1990, pp. 245-258.
28. _, An integral invariance principle for differential inclusions with application in adaptive control, SIAM J. Control & Optim. 36 (1998) 960-980.
29. S. Sastry, Nonlinear Systems: Analysis, Stability and Control, Springer-Verlag, New York, 1999.
30. G. V. Smirnov, Introduction to the Theory of Differential Inclusions, American Mathematical Society, Providence, 2002.
31. p, stability, IEEE Trans. Auto. Control AC-44 (1999) 2169-2170.
32. W. Walter, Ordinary Differential Equations, Springer-Verlag, New York, 1998.
33. J. Zabczyk, Mathematical Control Theory: An Introduction, Birkhäuser, Boston, 1992.