Abstract
Necessary and sufficient conditions are given for a nonlinear discrete-time system to be feedback equivalent to a controllable linear system. Some preliminary work on the effects of sampling on feedback linearizability is reported.
This work was supported in part by a NATO Postdoctoral Fellowship awarded in 1984 and in part by the National Science Foundation under Contract No. ECS-85-05318.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Cheng, D., T. Tarn, and A. Isidori, 1985, “Global Feedback Linearization of Nonlinear Systems,” IEEE Trans. Automat. Contd., 30, 808–811.
Dayawansa, W., D. Elliot, and W. M. Boothby, 1985, “Global Linearization by Feedback and State Transformation,” Poc. 25th IFFE Conf. Decision and Control, Ft. Lauderdale, FL, Dec. 11–13.
Hunt, L. and R. Su, 1981, “Local Transformations for Multi-Input Nonlinear Systems,” Proc. Joint Automatic Control Prof., Charlottesville, VA.
Jakubczyk, B. and W. Respondek, 1980, “On the Linearization of Control Systems,” Bull. Acad. Polon. Sci. Set. Math. Astron. Physics’, 28, 517–522.
Krener, A. J., 1973, “On 1he Equivalence of Control Systems and the inearization of Nonlinear Systems,” SIAM J. Control, 11, 670–676.
Lee, H.-G. and S. Marcus, 1985, “Approximate and Local Linearizability of Nonlinear Discrete-Time Systems,” to appear in Int. J. Control.
Monaco, S. and D. Normand-Cyrot, 1983, “The Immersion Under Feedback of a Multidimen-sional Discrete-Time Nonlinear System into a Linear System,” Int. J. Control, 38, 1.
Monaco, S. and D. Normand-Cyrot, 1985a, “Invariant Distributions Under Sampling,” Proc. of Conf. Mathematical Theory of Networks and Systems, Stockholm, June 1985.
Monaco, S. and D. Normand-Cyrot, 1985b, “On the Sampling of a Linear Analytic System,” Proc. 24th IEEE Conf. Decision and Control, Ft. Lauderdale, FL, 1457–1461.
Monaco, S. and D. Normand-Cyrot, 1985c, “Nonlinear Systems in Discrete Time,” to appear in Algebraic and Geometric Methods in Automatic Control
M. Fliess and H. Hazewinkel (Eds.), Riedel, Dordrecht, 1986. Respondek, W., 1985, “Global Aspects of Linearization, Equivalence to Polynomial Forms and Decomposition of Nonlinear Con-trol Systems,” to appear in Proc. of the Conf. on Algebraic and Geometric Methods Automatic Control, Paris, France.
Sontag, E., 1984a, “A concept of local observability,” Syst. and Contr. Lett., vol. 5, 1, Oct., 41–47.
Sontag, E., 1984b, “Remarks on Input/Output Linearization,” revised version of paper presented at 23rd IEEE Conf. on Decision and Control, Las Vegas, NV, Dec. 1984.
Sontag, E., 1985, “Orbit Theorems and Sampling,” to appear in Algebraic and Geometric Methods in Automatic Control.
M. Fliess and M. Hazewinkel (Eds.), Reidel, Dordrecht, 1986. van der Schaft, A. J., 1982, “Observability and Controllability for Smooth Nonlinear Systems,” SIAM J. Control and Optimi-zation, 20, 3, 338–354.
van der Schaft, A. J., 1984, “Linearization and Input-Output Decoupling for General Nonlinear Systems,” Syst. and Contr. Lett., 27–33.
Shor, M., 1986, Masters Thesis, Dept. of Electrical and Computer Engineering, University of Illi-nois at Urbana-Champaign, December.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1986 Springer Science+Business Media Dordrecht
About this paper
Cite this paper
Grizzle, J.W. (1986). Feedback Linearization of Discrete-Time Systems. In: Bensoussan, A., Lions, J.L. (eds) Analysis and Optimization of Systems. Lecture Notes in Control and Information Sciences, vol 83. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0007564
Download citation
DOI: https://doi.org/10.1007/BFb0007564
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-16729-7
Online ISBN: 978-3-540-39856-1
eBook Packages: Springer Book Archive