Free access
Issue
ESAIM: COCV
Volume 8, 2002
A tribute to JL Lions
Page(s) 703 - 713
DOI http://dx.doi.org/10.1051/cocv:2002035
Published online 15 August 2002
  1. C. Berrou and A. Glavieux, Near-optimum error-correcting coding and decoding: Turbo-codes. IEEE Trans. Communicat. 44 (1996) 1261-1271. [CrossRef]
  2. R.E. Blahut, Theory and Practice of Error Control Codes. Addison-Wesley (1983).
  3. N. Bourbaki, Algèbre, Chap. 2. Hermann (1970).
  4. G. Cohen, J.-L. Dornstetter and P. Godlewski, Codes correcteurs d'erreurs. Masson (1992).
  5. R.M. Cohn, Difference Algebra. Interscience (1965).
  6. A. Dholakia, Introduction to Convolutional Codes with Applications. Kluwer (1994).
  7. F. Fagnani and S. Zampieri, System-theoretic properties of convolutional codes over rings. IEEE Trans. Inform. Theory 47 (2001) 2256-2274. [CrossRef] [MathSciNet]
  8. M. Fliess, Automatique en temps discret et algèbre aux différences. Forum Math. 2 (1990) 213-232. [CrossRef] [MathSciNet]
  9. M. Fliess, Some basic structural properties of generalized linear systems. Systems Control Lett. 15 (1990) 391-396. [CrossRef] [MathSciNet]
  10. M. Fliess, A remark on Willems' trajectory characterization of linear controllability. Systems Control Lett. 19 (1992) 43-45. [CrossRef] [MathSciNet]
  11. M. Fliess, Reversible linear and nonlinear discrete-time dynamics. IEEE Trans. Automat. Control 37 (1992) 1144-1153. [CrossRef] [MathSciNet]
  12. M. Fliess, Une interprétation algébrique de la transformation de Laplace et des matrices de transfert. Linear Algebra Appl. 203-204 (1994) 429-442. [CrossRef]
  13. M. Fliess, Variations sur la notion de contrôlabilité, in Journée Soc. Math. France. Paris (2000) 47-86.
  14. M. Fliess and H. Bourlès, Discussing some examples of linear system interconnections. Systems Control Lett. 27 (1996) 1-7. [CrossRef] [MathSciNet]
  15. M. Fliess, J. Lévine, P. Martin and P. Rouchon, Flatness and defect of non-linear systems: Introductory theory and applications. Internat. J. Control 61 (1995) 1327-1361. [CrossRef] [MathSciNet]
  16. M. Fliess and R. Marquez, Continuous-time linear predictive control and flatness: A module-theoretic setting with examples. Internat. J. Control 73 (2000) 606-623. [CrossRef] [MathSciNet]
  17. M. Fliess and R. Marquez, Une approche intrinsèque de la commande prédictive linéaire discrète. APII J. Europ. Syst. Automat. 35 (2001) 127-147.
  18. M. Fliess, R. Marquez, E. Delaleau and H. Sira-Ramírez, Correcteurs proportionnels-intégraux généralisés. ESAIM: COCV 7 (2002) 23-41. [CrossRef] [EDP Sciences]
  19. M. Fliess, R. Marquez and H. Mounier, An extension of predictive control, PID regulators and Smith predictors to some linear delay systems. Internat. J. Control (to appear).
  20. M. Fliess and H. Mounier, Controllability and observability of linear delay systems: An algebraic approach. ESAIM: COCV 3 (1998) 301-314. [CrossRef] [EDP Sciences]
  21. G.D. Forney Jr., Convolutional codes I: Algebraic structure. IEEE Trans. Inform. Theory 16 (1970) 720-738. [CrossRef]
  22. G.D. Forney Jr., Minimal bases of rational vector spaces, with applications to multivariable linear systems. SIAM J. Control 13 (1975) 493-520. [CrossRef] [MathSciNet]
  23. G.D. Forney Jr., Algebraic structure of convolutional codes and algebraic system theory, in Mathematical System Theory - The Influence of R.E. Kalman, edited by A.C. Antoulas. Springer (1991) 527-557.
  24. G.D. Forney Jr. and M.D. Trott, The dynamics of group codes: State-space, trellis diagrams and canonical encoders. IEEE Trans. Inform. Theory 39 (1993) 1491-1513. [CrossRef] [MathSciNet]
  25. G.D. Forney Jr., B. Marcus, N.T. Sindhushayana and M. Trott, A multilingual dictionary: System theory, coding theory, symbolic dynamics and automata theory, in Different Aspects of Coding Theory. Proc. Symp. Appl. Math. 50; Amer. Math. Soc. (1995) 109-138.
  26. R. Johannesson and K.Sh. Zigangirov, Fundamentals of Convolutional Coding. IEEE Press (1999).
  27. T. Kailath, Linear Systems. Prentice-Hall (1979).
  28. E.W. Kamen, P.P. Khargonekar and K.R. Poola, A transfer-function approach to linear time-varying discrete-time systems. SIAM J. Control Optim. 23 (1985) 550-565. [CrossRef] [MathSciNet]
  29. T.Y. Lam, Lectures on Rings and Modules. Springer (1999).
  30. S. Lin and D.J. Costello Jr., Error Control Coding: Fundamentals and Applications. Prentice-Hall (1983).
  31. J.H. van Lint, Introduction to Coding Theory, Formula Edition. Springer (1999).
  32. H.-A. Loeliger, G.D. Forney Jr., T. Mittelholzer and M.D. Trott, Minimality and observability of group systems. Linear Algebra Appl. 205-206 (1994) 937-963. [CrossRef]
  33. J.L. Massey and M.K. Sain, Codes, automata and contnuous systems: Explicit interconnections. IEEE Trans. Automat. Control 12 (1967) 644-650. [CrossRef]
  34. R.J. McEliece, The algebraic theory of convolutional codes, in Handbook of Coding Theory, Vol. 1, edited by V. Pless and W.C. Huffman. Elsevier (1998) 1065-1138.
  35. J.C. McConnel and J.C. Robson, Noncommutative Noetherian Rings. Wiley (1987).
  36. H. Mounier, P. Rouchon and J. Rudolph, Some examples of linear systems with delays. APII J. Europ. Syst. Automat. 31 (1997) 911-925.
  37. P. Piret, Convolutional Codes, an Algebraic Approach. MIT Press (1988).
  38. J. Rosenthal, Connections between linear systems and convolutional codes, in Codes, Systems and Graphical Models, edited by B. Marcus and J. Rosenthal. Springer (2000) 39-66.
  39. J. Rosenthal, J.M. Schumacher and E.V. York, On behaviors and convolutional codes. IEEE Trans. Informat. Theory 42 (1996) 1881-1891. [CrossRef]
  40. J. Rosenthal and E.V. York, BCH convolutional codes. IEEE Trans. Inform. Theory 45 (1999) 1833-1844. [CrossRef] [MathSciNet]
  41. J. Rotman, An Introduction to Homological Algebra. Academic Press (1979).
  42. A.J. Viterbi and J.K. Omura, Principles of Digital Communication and Coding. McGraw-Hill (1979).
  43. L. Weiss, Controllability, realization and stability of discrete-time systems. SIAM J. Control 10 (1972) 230-251. [CrossRef] [MathSciNet]
  44. J.C. Willems, Paradigms and puzzles in the theory of dynamical systems. IEEE Trans. Automat. Control 36 (1991) 259-294. [CrossRef] [MathSciNet]
  45. G. Zémor, Cours de cryptographie. Cassini (2000).