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1995 | 32 | 1 | 123-137
Tytuł artykułu

Global linearization of nonlinear systems - A survey

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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.
Rocznik
Tom
32
Numer
1
Strony
123-137
Opis fizyczny
Daty
wydano
1995
Twórcy
  • Institute of Information Theory and Automation, Academy of Sciences of the Czech Republic, P.O. Box 18, 182 08 Prague 8, Czech Republic
Bibliografia
  • [1] W. M. Boothby, Some comments on global linearization of nonlinear systems, Systems Control Lett. 4 (1984), 143-149.
  • [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] R. W. Brockett, Feedback invariants for nonlinear systems, Prepr. IFAC Congr., Helsinki, Finland, 1978, 1115-1120.
  • [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] P. Brunovský, A classification of linear controllable systems, Kybernetika 1970, 173-180.
  • [6] C. Byrnes and A. Isidori, Asymptotic stabilization of minimal phase nonlinear systems, IEEE Trans. Automat. Contr. 36 (1991), 1122-1137.
  • [7] B. Charlet, J. Lévine and R. Marino, On dynamic feedback linearization, Systems Control Lett. 13 (1989), 143-151.
  • [8] B. Charlet, J. Lévine and R. Marino, Sufficient conditions for dynamic state feedback linearization, SIAM J. Control Optim. 29 (1991), 38-57.
  • [9] S. Čelikovský, On the global linearization of bilinear systems, Systems Control Lett. 15 (1990), 433-439.
  • [10] S. Čelikovský, On the global linearization of nonhomogeneous bilinear systems, ibid. 18 (1992), 397-402.
  • [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] S. Čelikovský, Global state linearization of multi-input bilinear systems, in: Proc. 1st Asian Control Conf., Tokyo, July 1994, Vol. 3, 133-136.
  • [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] 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.
  • [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.
  • [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] W. Dayawansa, W. M. Boothby and D. L. Elliot, Global state and feedback equivalence of nonlinear systems, Systems Control Lett. 6 (1985), 229-234.
  • [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] L. R. Hunt, R. Su and G. Meyer, Global transformation of nonlinear systems, IEEE Trans. Automat. Control AC-28 (1983), 24-31.
  • [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.
  • [21] A. Isidori and A. Ruberti, On the synthesis of linear input-output responses for nonlinear systems, Systems Control Lett. 4 (1984), 17-22.
  • [22] A. Isidori, Nonlinear Control Systems: An Introduction, 2nd ed., Springer, Berlin, 1989.
  • [23] B. Jakubczyk and W. Respondek, On linearization of control systems, Bull. Acad. Polon. Sci. Sér. Sci. Math. 28 (1980), 517-522.
  • [24] A. J. Krener, On the equivalence of control systems and the linearization of nonlinear systems, SIAM J. Control Optim. 11 (1973), 670-676.
  • [25] A. J. Krener, A decomposition theory for differentiable systems, ibid. 15 (1977), 813-829.
  • [26] A. J. Krener and A. Isidori, Linearization by output injection and nonlinear oservers, Systems Control Lett. 3 (1983), 47-52.
  • [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.
  • [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.
  • [29] H. Nijmeijer and A. J. van der Shaft, Nonlinear Dynamical Control Systems, Springer, Berlin, 1990.
  • [30] R. S. Palais, A global formulation of the Lie theory of transformation groups, Mem. Amer. Math. Soc. 22 (1957).
  • [31] W. Respondek, Geometric methods in linearization of control systems, in: Mathematical Control Theory, Banach Center Publ. 14, PWN Warszawa, 1985, 453-467.
  • [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.
  • [33] M. Sampei and K. Furuta, On time scaling for nonlinear systems: application to linearization, IEEE Trans. Automat. Control AC-31 (1986), 459-462.
  • [34] R. Su (1982), On the linear equivalents of nonlinear systems, Systems Control Lett. 2 (1982), 48-52.
  • [35] H. J. Sussmann, An extension of a theorem of Nagano on transitive Lie algebras, Proc. Amer. Math. Soc. 45 (1974), 349-356.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-bcpv32z1p123bwm
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