Exploitation of Ljapunov theory for verifying self-stabilizing algorithms

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 1914, Issue , 2000, Pages 209-222

  Theel, Oliver ^a  

^a DARMSTADT UNIVERSITY OF TECHNOLOGY   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTATION THEORY; DISTRIBUTED COMPUTER SYSTEMS; STABILIZATION;

DESIGN STRATEGIES; ENGINEERING DOMAINS; FEEDBACK SYSTEMS; INITIAL STATE; NON-TRIVIAL; SELF STABILIZATION; SELF-STABILIZING ALGORITHM; STABILIZING PROPERTIES;

ALGORITHMS;

EID: 84958741298     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/3-540-40026-5_14     Document Type: Conference Paper

References (21)

1. A. Arora. Encyclopedia of Distributed Computing, chapter Stabilization. Kluwer Academic Publishers, 1999.
2. J. Desel, E. Kindler, T. Vesper, and R. Walter. A simplified proof for a self- stabilizing protocol: A Game of Cards. Information Processing Letters, 54:327¬328, 1995.
3. E. Dijkstra. Guarded commands, nondeterminacy, and formal derivation of pro¬grams. Communications of the Association for Computing Machinery, 18(8):453- 457, Aug. 1975.
4. E. W. Dijkstra. Self stabilizing systems in spite of distributed control. Commun. ACM, 17(11):(i 13 il l. 1974.
5. E. W. Dijkstra. A belated proof of self stabilization. Distributed Computing, 1:5-6, 1986.
6. O. Follinger. Nichtlineare Regelungen I (in Germ,an). R. Oldenburg Verlag, Mu¬nich, Germany, 1998.
7. M. G. Gouda and T. Herman. Stabilizing Unison. IPL, pages 171-175, August 1990.
8. M. G. Gouda and N. J. Multari. Stabilizing communication protocols. IEEE Transactions on Computers, 40(4):448-458, Apr. 1991.
9. W. Hahn. Stability of Motion. Springer-Verlag, 1967.
10. R. Isermann. Digitale Reyelsysteme, Band I (in Germ,an). Springer-Verlag, New York, 1988. ISBN 0-387-16596-7.
11. R. E. Kalman and J. E. Bertram. Control System Analysis and Design Via the “Second Method” of Lyapunov - Part I: Continuous-Time Systems. Transactions of the ASME, Journal of Basic Engineering, 82:371-393, June 1960.
12. R. E. Kalman and J. E. Bertram. Control System Analysis and Design Via the “Second Method” of Lyapunov - Part II: Discrete-Time Systems. Transactions of the ASME, Journal of Basic Engineering, 82:394-400, June 1960.
13. J. L. W. Kessels. An exercise in proving self-stabilization with a variant function. Information Processing Letters, 29:39-42, 1988.
14. M. A. Ljapunov. Probleme general de la stabilite du movement. Ann. Fac. Sci. Toulouse, 9:203-474, 1907.
15. D. Mandrioli and C. Ghezzi. Theoretical Foundations of Computer Science. John Wiley and Sons, 1987.
16. M. Schneider. Self-stabilization. ACM Computing Surveys, 25(l):45-67, 1993.
17. G. Tel. Introduction to Distributed Algorithms. Cambridge University Press, 1994.
18. O. Theel. Verification of Dijkstra’s Self-Stabilizing Token Ring Algorithm by Means of Non-Linear Control System Analysis. Technical Report TUD-BS-2000- 02, Darmstadt University of Technology, Dept, of Computer Science, Institute for System Architecture, D-64283 Darmstadt, Germany, March 2000. Accepted for Publication at the Intern. Symposium on Computational Intelligence (CI’OO) being part of the Intern. ICSC Congress on Intelligent Systems and Applications (ISA 2000), Wollongong, Australia, December 12-15, 2000.
19. O. Theel and F. C. Gartner. An Exercise in Proving Convergence through Transfer Functions. In Proc. of the 4th Workshop on Self-Stabilizing Systems (WSS’99), being part of the 19th, International Conference on, Distributed Computer Systems (ICDCS’99), Austin, TX, U.S.A., pages 41-47. IEEE, June 1999.
20. V. I. Utkin. Variable Structure Systems with Sliding Modes. IEEE Transactions on Automatic Control, 22:212-222, 1977.
21. J. C. Willems. The Analysis of Feedback System,s. Number 62 in Research Monograph. The M.I.T. Press, Cambridge, MA, U.S.A., 1971.