Global linearization of nonlinear systems - A survey
Čelikovský, Sergej
Banach Center Publications, Tome 31 (1995), p. 123-137 / Harvested from The Polish Digital Mathematics Library

A survey of the global linearization problem is presented. Known results are divided into two groups: results for general affine nonlinear systems and for bilinear systems. In the latter case stronger results are available. A comparision of various linearizing transformations is performed. Numerous illustrative examples are included.

Publié le : 1995-01-01
EUDML-ID : urn:eudml:doc:262754
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     title = {Global linearization of nonlinear systems - A survey},
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     volume = {31},
     year = {1995},
     pages = {123-137},
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Čelikovský, Sergej. Global linearization of nonlinear systems - A survey. Banach Center Publications, Tome 31 (1995) pp. 123-137. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-bcpv32z1p123bwm/

[000] [1] W. M. Boothby, Some comments on global linearization of nonlinear systems, Systems Control Lett. 4 (1984), 143-149. | Zbl 0538.93027

[001] [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.

[002] [3] R. W. Brockett, Feedback invariants for nonlinear systems, Prepr. IFAC Congr., Helsinki, Finland, 1978, 1115-1120.

[003] [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.

[004] [5] P. Brunovský, A classification of linear controllable systems, Kybernetika 1970, 173-180. | Zbl 0199.48202

[005] [6] C. Byrnes and A. Isidori, Asymptotic stabilization of minimal phase nonlinear systems, IEEE Trans. Automat. Contr. 36 (1991), 1122-1137. | Zbl 0758.93060

[006] [7] B. Charlet, J. Lévine and R. Marino, On dynamic feedback linearization, Systems Control Lett. 13 (1989), 143-151. | Zbl 0684.93043

[007] [8] B. Charlet, J. Lévine and R. Marino, Sufficient conditions for dynamic state feedback linearization, SIAM J. Control Optim. 29 (1991), 38-57. | Zbl 0739.93021

[008] [9] S. Čelikovský, On the global linearization of bilinear systems, Systems Control Lett. 15 (1990), 433-439. | Zbl 0732.93012

[009] [10] S. Čelikovský, On the global linearization of nonhomogeneous bilinear systems, ibid. 18 (1992), 397-402. | Zbl 0763.93028

[010] [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.

[011] [12] S. Čelikovský, Global state linearization of multi-input bilinear systems, in: Proc. 1st Asian Control Conf., Tokyo, July 1994, Vol. 3, 133-136.

[012] [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.

[013] [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. | Zbl 0666.93054

[014] [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. | Zbl 0666.93019

[015] [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.

[016] [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. | Zbl 0577.93029

[017] [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.

[018] [19] L. R. Hunt, R. Su and G. Meyer, Global transformation of nonlinear systems, IEEE Trans. Automat. Control AC-28 (1983), 24-31. | Zbl 0502.93036

[019] [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. | Zbl 0481.93037

[020] [21] A. Isidori and A. Ruberti, On the synthesis of linear input-output responses for nonlinear systems, Systems Control Lett. 4 (1984), 17-22. | Zbl 0551.93032

[021] [22] A. Isidori, Nonlinear Control Systems: An Introduction, 2nd ed., Springer, Berlin, 1989.

[022] [23] B. Jakubczyk and W. Respondek, On linearization of control systems, Bull. Acad. Polon. Sci. Sér. Sci. Math. 28 (1980), 517-522. | Zbl 0489.93023

[023] [24] A. J. Krener, On the equivalence of control systems and the linearization of nonlinear systems, SIAM J. Control Optim. 11 (1973), 670-676. | Zbl 0243.93009

[024] [25] A. J. Krener, A decomposition theory for differentiable systems, ibid. 15 (1977), 813-829. | Zbl 0361.93023

[025] [26] A. J. Krener and A. Isidori, Linearization by output injection and nonlinear oservers, Systems Control Lett. 3 (1983), 47-52. | Zbl 0524.93030

[026] [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. | Zbl 0796.93049

[027] [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. | Zbl 0693.93030

[028] [29] H. Nijmeijer and A. J. van der Shaft, Nonlinear Dynamical Control Systems, Springer, Berlin, 1990.

[029] [30] R. S. Palais, A global formulation of the Lie theory of transformation groups, Mem. Amer. Math. Soc. 22 (1957). | Zbl 0178.26502

[030] [31] W. Respondek, Geometric methods in linearization of control systems, in: Mathematical Control Theory, Banach Center Publ. 14, PWN Warszawa, 1985, 453-467. | Zbl 0573.93028

[031] [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. | Zbl 0605.93033

[032] [33] M. Sampei and K. Furuta, On time scaling for nonlinear systems: application to linearization, IEEE Trans. Automat. Control AC-31 (1986), 459-462. | Zbl 0611.93037

[033] [34] R. Su (1982), On the linear equivalents of nonlinear systems, Systems Control Lett. 2 (1982), 48-52. | Zbl 0482.93041

[034] [35] H. J. Sussmann, An extension of a theorem of Nagano on transitive Lie algebras, Proc. Amer. Math. Soc. 45 (1974), 349-356. | Zbl 0301.58003