Global linearization of nonlinear systems - A survey

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1. [1] W. M. Boothby, Some comments on global linearization of nonlinear systems, Systems Control Lett. 4 (1984), 143-149. Zbl0538.93027
2. [2] W. M. Boothby, Global feedback linearizability of locally linearizable systems, in: Algebraic and Geometric Methods in Nonlinear Control Theory, M. Fliess and M. Hazewinkel (eds.), Reidel, Dordrecht, 1986, 243-246. 
3. [3] R. W. Brockett, Feedback invariants for nonlinear systems, Prepr. IFAC Congr., Helsinki, Finland, 1978, 1115-1120. 
4. [4] R. W. Brockett, On the algebraic structure of bilinear systems, in: Theory and Applications of Variable Structure Systems, R. R. Mohler and A. Ruberti (eds.), Academic Press, New York, 1972, 153-168. 
5. [5] P. Brunovský, A classification of linear controllable systems, Kybernetika 1970, 173-180. Zbl0199.48202
6. [6] C. Byrnes and A. Isidori, Asymptotic stabilization of minimal phase nonlinear systems, IEEE Trans. Automat. Contr. 36 (1991), 1122-1137. Zbl0758.93060
7. [7] B. Charlet, J. Lévine and R. Marino, On dynamic feedback linearization, Systems Control Lett. 13 (1989), 143-151. Zbl0684.93043
8. [8] B. Charlet, J. Lévine and R. Marino, Sufficient conditions for dynamic state feedback linearization, SIAM J. Control Optim. 29 (1991), 38-57. Zbl0739.93021
9. [9] S. Čelikovský, On the global linearization of bilinear systems, Systems Control Lett. 15 (1990), 433-439. Zbl0732.93012
10. [10] S. Čelikovský, On the global linearization of nonhomogeneous bilinear systems, ibid. 18 (1992), 397-402. Zbl0763.93028
11. [11] S. Čelikovský, On the relation between local and global linearization of bilinear systems, in: Systems Structure and Control, V. Strejc (ed.), Pergamon Press, Oxford, 1992, 172-175. 
12. [12] S. Čelikovský, Global state linearization of multi-input bilinear systems, in: Proc. 1st Asian Control Conf., Tokyo, July 1994, Vol. 3, 133-136. 
13. [13] D. Cheng, T. J. Tarn and A. Isidori, Global linearization of nonlinear systems, in: Proc. 23rd. IEEE Conference on Decision and Control, 1984, 74-83. 
14. [14] D. Cheng, T. J. Tarn and A. Isidori, Global external linearization of nonlinear systems via feedback, IEEE Trans. Automat Control AC-30 (1985), 808-811. Zbl0666.93054
15. [15] D. Cheng, A. Isidori, W. Respondek and T. J. Tarn, Exact linearization of nonlinear systems with outputs, Math. Systems Theory, 21 (1988), 63-83. Zbl0666.93019
16. [16] D. Claude, Everything you always wanted to know about linearization but were afraid to ask, in: Algebraic and Geometric Methods in Nonlinear Control Theory, M. Fliess and M. Hazewinkel (eds.), Reidel, Dordrecht, 1986, 181-226. 
17. [17] W. Dayawansa, W. M. Boothby and D. L. Elliot, Global state and feedback equivalence of nonlinear systems, Systems Control Lett. 6 (1985), 229-234. Zbl0577.93029
18. [18] W. Dayawansa, W. M. Boothby and D. L. Elliot, Global linearization by feedback and state transformations, in: Proc. 24th IEEE Conf. on Decision and Control, Dec. 1985, 1042-1049. 
19. [19] L. R. Hunt, R. Su and G. Meyer, Global transformation of nonlinear systems, IEEE Trans. Automat. Control AC-28 (1983), 24-31. Zbl0502.93036
20. [20] A. Isidori, J. A. Krener, C. Gori Giorgi and S. Monaco, Nonlinear Decoupling via feedback: a differential geometric approach, IEEE Trans. Automat. Control AC-26 (1981), 331-345. Zbl0481.93037
21. [21] A. Isidori and A. Ruberti, On the synthesis of linear input-output responses for nonlinear systems, Systems Control Lett. 4 (1984), 17-22. Zbl0551.93032
22. [22] A. Isidori, Nonlinear Control Systems: An Introduction, 2nd ed., Springer, Berlin, 1989. 
23. [23] B. Jakubczyk and W. Respondek, On linearization of control systems, Bull. Acad. Polon. Sci. Sér. Sci. Math. 28 (1980), 517-522. Zbl0489.93023
24. [24] A. J. Krener, On the equivalence of control systems and the linearization of nonlinear systems, SIAM J. Control Optim. 11 (1973), 670-676. Zbl0243.93009
25. [25] A. J. Krener, A decomposition theory for differentiable systems, ibid. 15 (1977), 813-829. Zbl0361.93023
26. [26] A. J. Krener and A. Isidori, Linearization by output injection and nonlinear oservers, Systems Control Lett. 3 (1983), 47-52. Zbl0524.93030
27. [27] R. Marino, W. Respondek and A. J. van der Shaft, Equivalence of nonlinear control systems to input-output prime forms, SIAM J. Control Optim. 32 (1994), 387-407. Zbl0796.93049
28. [28] R. Marino, W. Respondek and A. J. van der Shaft, Almost disturbance decoupling for single-input single output nonlinear systems, IEEE Trans. Automat. Control 34 (1989), 1013-1017. Zbl0693.93030
29. [29] H. Nijmeijer and A. J. van der Shaft, Nonlinear Dynamical Control Systems, Springer, Berlin, 1990. 
30. [30] R. S. Palais, A global formulation of the Lie theory of transformation groups, Mem. Amer. Math. Soc. 22 (1957). Zbl0178.26502
31. [31] W. Respondek, Geometric methods in linearization of control systems, in: Mathematical Control Theory, Banach Center Publ. 14, PWN Warszawa, 1985, 453-467. Zbl0573.93028
32. [32] W. Respondek, Global aspects of linearization, equivalence to polynomial forms and decomposition of nonlinear systems, in: Algebraic and Geometric Methods in Nonlinear Control Theory, M. Fliess and M. Hazewinkel (eds.), Reidel, Dordrecht, 1986, 257-284. Zbl0605.93033
33. [33] M. Sampei and K. Furuta, On time scaling for nonlinear systems: application to linearization, IEEE Trans. Automat. Control AC-31 (1986), 459-462. Zbl0611.93037
34. [34] R. Su (1982), On the linear equivalents of nonlinear systems, Systems Control Lett. 2 (1982), 48-52. Zbl0482.93041
35. [35] H. J. Sussmann, An extension of a theorem of Nagano on transitive Lie algebras, Proc. Amer. Math. Soc. 45 (1974), 349-356. Zbl0301.58003

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