On dynamic feedback linearization of four-dimensional affine control systems with two inputs

 Access to full text

 Full (PDF)

1. [1] E. Aranda-Bricaire, C.H. Moog, J.-B. Pomet: An infinitesimal brunovsky form for nonlinear systems with applications to dynamic linearization, in Geometry in Nonlinear Control and Differential Inclusions, B. Jakuczyk, W. Respondek, and T. Rzezuchowski, eds., Banach Center Publications, 32, Warsaw, Poland, 1995, Institute of Mathematics, Polish Academy of Sciences, 19-33. Zbl0844.93024MR1364417
2. [2] E. Aranda-Bricaire, C.H. Moog, J.-B. Pomet: A linear algebraic framework for dynamic feedback linearization, IEEE Trans. Automat. Control, 40, 1995, 127-132. Zbl0844.93025MR1344331
3. [3] B. Bonnard: Feedback equivalence for nonlinear systems and the time-optimal control problem, SIAM J. on Control and Optim., 29, 1991, 1300-1321. Zbl0744.93033MR1132184
4. [4] R.W. Brockett: Feedback invariants for nonlinear systems, in IFAC World Congress, Helsinki, 1978, Birkäuser. Zbl0457.93028
5. [5] P. Brunovský: A classification of linear controllable systems, Kybernetica, 6, 1970, 176-188. Zbl0199.48202MR284247
6. [6] R.L. Bryant, S.S. Chern, R.B. Gardner, H.L. Goldschmitt, P.A. Griffiths: Exterior Differential Systems, Mathematical Sciences Research Institute Publications 18, Springer-Verlag, 1991. Zbl0726.58002MR714337
7. [7] B. Charlet, J. Lévine, R. Marino: Sufficient conditions for dynamic state feedback linearization, SIAM J. on Control and Optim., 29, 1991, 38-57. Zbl0739.93021MR1088218
8. [8] M. Fliess, J. Lévine, P. Martin, P. Rouchon: On differentially flat nonlinear systems, in Nonlinear Control Systems Design, M. Fliess, ed., Pergamon Press, 1992, 408-412. MR1181303
9. [9] M. Fliess, J. Lévine, P. Martin, P. Rouchon: Linéarisation par bouclage dynamique et transformations de Lie-Bäcklund, C. R. Acad. Sci., Paris, Série I, 317, 1993, 981-986. Zbl0796.93042MR1249373
10. [10] M. Fliess, J. Lévine, P. Martin, P. Rouchon: Towards a new differential geometric setting in nonlinear control, in Proc. International Geometrical Coll., Moscow, 1993. 
11. [11] M. Fliess, J. Lévine, P. Martin, P. Rouchon: Flatness and defect of nonlinear systems: Introductory theory and examples, Int. J. Control, 61, 1995, 1327-1361. Zbl0838.93022MR1613557
12. [12] L.R. Hunt, R. Su, G. Meyer: Design for multi-input nonlinear systems, in Differential Geometric Control Theory, R. Brockett, ed., Birkhäuser, 1983, 258-298. Zbl0543.93026MR708508
13. [13] B. Jakubczyk: Equivalence and invariants of nonlinear control systems, in Nonlinear Controllability and Optimal Control, H.J. Sussmann, ed., Marcel Dekker, New-York, 1990. Zbl0712.93027MR1061386
14. [14] B. Jakubczyk: Dynamic feedback equivalence of nonlinear control systems. Preprint, 1994. 
15. [15] B. Jakubczyk, W. Respondek: On linearization of control systems, Bull. Acad. Polonaise Sci. Ser. Sci. Math., 28, 1980, 517-522. Zbl0489.93023MR629027
16. [16] C. Leleu, J.-B. Pomet: A package in "maple" to decide on (x, u)-dynamic linearizability of control systems with four states and two inputs, rapport de recherche, INRIA, 1997, to appear. (URL: http://www.inria.fr/publications-eng.html). 
17. [17] J. Lévine, R. Marino: On dynamic feedback linearization on ℝ, in 29th IEEE Conf. on Decision & Control, 1990, 2088-2090. 
18. [18] P. Martin: Contribution à l'étude des systèmes différentiellement plats, PhD thesis, L'École Nationale Supérieure des Mines de Paris, 1992. 
19. [19] J.-B. Pomet: A differential geometric setting for dynamic equivalence and dynamic linearization, in Geometry in Nonlinear Control and Differential Inclusions, B. Jakuczyk, W. Respondek, T. Rzezuchowski, eds., Banach Center Publications 32, Warsaw, Poland, 1995, Institute of Mathematics, Polish Academy of Sciences, 319-339 Zbl0838.93019MR1364437
20. [20] J.-B. Pomet, C. H. Moog, E. Aranda-Bricaire: A non-exact Brunovsky form and dynamic feedback linearization, in 31st IEEE Conf. on Decision and Control, Tucson, U.S.A., Dec. 1992, 2012-2017. 
21. [21] J.-F. Pommaret: Partial Differential Equations and Group Theory, Mathematics and its Applications 293, Kluwer Academic Publishers, Dordrecht, Boston, London, 1994. Zbl0808.35002MR1308976
22. [22] P. Rouchon: Necessary condition and genericity of dynamic feedback linearization, Journal of Mathematical Systems, Estimation, and Control, 4, 1994, 1-14. Zbl0818.93012MR1646298
23. [23] W. Shadwick: Absolute equivalence and dynamic feedback linearization, Systems & Control Lett., 15, 1990, 35-39. Zbl0704.93037MR1065346
24. [24] W. Sluis: A necessary condition for dynamic feedback linearization, Systems & Control Lett., 21, 1993, 277-283. Zbl0793.93070MR1241406
25. [25] S. Sternberg: Lectures on Differential Geometry, Chelsea Publishing Co., New York, 2nd ed., 1983. Zbl0518.53001MR891190