Abstract
In this paper we show how it is possible to develop finite dimensional compensators which stabilize nonlinear infinite dimensional systems. Since our methods rely heavily on linear theory, we will begin by reviewing some of the linear results
Preview
Unable to display preview. Download preview PDF.
References
Curtain, R.F.: Finite dimensional compensator design for parabolic systems with point and boundary input, IEEE Trans. Automat. Control Vol. AC-26 (1982), 98–104.
Curtain, R.F.: Compensators for infinite dimensional linear systems: a survey, to appear in the special issue of the Journal of the Franklin Institute on Distributed Parameter Systems.
Curtain, R.F., A.J. Pritchard: Infinite dimensional linear systems theory, Lectures Notes in Control and Information Sciences, Vol. 8, Springer Verlag, 1978.
Ichikawa, A., A.J. Pritchard: Existence, uniqueness and stability of nonlinear evolution equations, J. Math. Anal. and Appl., Vol. 68, No. 2, (April 1979), 454–476.
Kato, T.: Perturbation theory of linear operators, Springer Verlag, 1966.
Pritchard, A.J., J. Zabczyk: Stability and stabilizability of infinite dimensional systems, SIAM Review, Vol. 23 (1981), 25–52.
Slemrod, M.: Asymptotic behaviour of Co-semigroups as determined by the spectrum of the generator, Indiana Univ. Math. J. 25 (1976), 783–791.
Schumacher, J.M.: Compensator synthesis using (C,A,B) pairs, IEEE Trans. Automat. Control, Vol. AC-25 (1980), 1133–1138.
Schumacher, J.M.: A direct approach to compensator design for distributed parameter systems, to appear in SIAM J. Control and Optimization.
Triggiani, R., A. J. Pritchard, Stabilizability in Banach space, Control Theory Centre Report No. 35, University of Warwick., U.K.
Willems, J.C.: Almost A(mod B)-Invariant subspaces, Asterisque 75–76 (1980), 239–248.
Yoside, K.: Functional analysis, Springer Verlag 1965.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1983 Springer-Verlag
About this paper
Cite this paper
Chapman, M.J., Pritchard, A.J. (1983). Finite dimensional compensators for nonlinear infinite dimensional systems. In: Kappel, F., Kunisch, K., Schappacher, W. (eds) Control Theory for Distributed Parameter Systems and Applications. Lecture Notes in Control and Information Sciences, vol 54. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0043939
Download citation
DOI: https://doi.org/10.1007/BFb0043939
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-12554-9
Online ISBN: 978-3-540-38647-6
eBook Packages: Springer Book Archive