Abstract
The purpose of this paper is to show that three possible characterizations of the notion of "transmission zero", namely "pole" of the inverse system, zero-output-constrained dynamics and unobservable dynamics under certain state-feedback, which are equivalent for any invertible linear system, may have different analogues for nonlinear input-affine systems. It is also shown that some nonlinear versions of the so-called structure algorithm, proposed by Hirschorn and Singh, may be successfully used in this framework.
Preview
Unable to display preview. Download preview PDF.
References
A.J.Krener, A.Isidori: Nonlinear zero distributions, 19th IEEE Conf. Decision and Control, (1980).
C.Byrnes, A.Isidori: A frequency domain philosophy for nonlinear systems, with applications to stabilization and adaptive control, 23rd IEEE Conf. Decision and Control, (1984), pp. 1569–1573.
R. Marino: High-gain feedback in non-linear control systems, Int. J. Control, 42 (1985), pp. 1369–1385.
A. Isidori: Control of Nonlinear Systems via dynamic state-feedback, Algebraic and Geometric Methos in Nonlinear Control Theory (M. Hazewinkel and M. Fliess, eds.), Reidel (1986).
A. Isidori: Nonlinear control systems: an introduction, Lecture Notes in Control and Information Sciences, Vol. 72, Springer Verlag (1985).
M. Fliess: A note on the invertibility of nonlinear input-output differential systems, Systems and Control Lett., (1986), to appear.
C. Byrnes, A. Isidori: Global feedback stabilization of nonlinear systems, 24th IEEE Conf. Decision and Control, (1985).
L.M. Silverman: Inversion of multivariable linear systems, IEEE Trans. Automatic Control, AC-14 (1969), pp. 270–276.
R.M. Hirschorn: Invertibility of multivariable nonlinear control systems, IEEE Trans. Automatic Control, AC-24 (1979), pp. 855–865.
S.N. Singh: A modified algorithm for invertibility in nonlinear systems, IEEE Trans. Automatic Control, AC-26 (1981), pp. 595–598.
A.J. Krener, A. Isidori, C. Gori-Giorgi, S. Monaco: Nonlinear decoupling via feedback: a differential-geometric approach, IEEE Trans. Automatic Control, AC-26 (1981), pp.331–345.
J. Descusse, C.H. Moog: Decoupling with dynamic compensation for strong invertible affine nonlinear systems, Int. J. of Control, 42 (1985), pp. 1387–1398.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1988 Springer-Verlag
About this paper
Cite this paper
Isidori, A., Moog, C.H. (1988). On the nonlinear equivalent of the notion of transmission zeros. In: Byrnes, C.I., Kurzhanski, A.B. (eds) Modelling and Adaptive Control. Lecture Notes in Control and Information Sciences, vol 105. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0043181
Download citation
DOI: https://doi.org/10.1007/BFb0043181
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-19019-6
Online ISBN: 978-3-540-38904-0
eBook Packages: Springer Book Archive