Abstract
We show that a linear time-varying single-input system of state dimension n which is N-controllable (N ≥ n) can be transformed into a chain of integrators by an exogenous dynamic feedback of size N — n and a change of coordinates.
Preview
Unable to display preview. Download preview PDF.
References
P. Brunovský. A classification of linear controllable systems. Kybernetika, 6(3):173–188, 1970.
M. Fliess, J. Lévine, Ph. Martin, and P. Rouchon. A Lie-Bäcklund approach to equivalence and flatness of nonlinear systems. IEEE Trans. Automat. Control, 44:922–937, 1999.
B. Jakubczyk and W. Respondek. On linearization of control systems. Bull. Acad. Pol. Sci. Ser. Sci. Math., 28:517–522, 1980.
T. Kailath. Linear Systems. Prentice-Hall, 1980.
E. W. Kamen, P. P. Khargonekar, and K. R. Poolla. A transfer-function approach to linear time-varying discrete-time systems. SIAM J. Control & Opt., 23(4):550–565, 1985.
B. Malgrange. Lettre du 26 janvier. Communication personnelle.
Ph. Martin, R. Murray, and P. Rouchon. Flat systems. In Proc. of the 4th European Control Conf., pages 211–264, Brussels, 1997. Plenary lectures and Mini-courses.
A. S. Morse and L. M. Silverman. Structure of index-invariant systems. SIAM J. Control, 11(2):215–225, 1973.
L. M. Silverman and H. E. Meadows. Controllability and observability in time-variable linear systems. SIAM J. Control, 5:64–73, 1967.
E. D. Sontag. Controllability and linearized regulation. IEEE Trans. Automat. Control, AC-32(10):877–888, 1987.
E. D. Sontag. Mathematical Control Theory. Springer, 2nd edition, 1991.
W. A. Wolovich. On the stabilization of controllable systems. IEEE Trans. Automat. Control, AC-13:569–572, 1968.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2001 Springer-Verlag London Limited
About this paper
Cite this paper
Malrait, F., Martin, P., Rouchon, P. (2001). Dynamic feedback transformations of controllable linear time-varying systems. In: Isidori, A., Lamnabhi-Lagarrigue, F., Respondek, W. (eds) Nonlinear control in the year 2000 volume 2. Lecture Notes in Control and Information Sciences, vol 259. Springer, London. https://doi.org/10.1007/BFb0110291
Download citation
DOI: https://doi.org/10.1007/BFb0110291
Published:
Publisher Name: Springer, London
Print ISBN: 978-1-85233-364-5
Online ISBN: 978-1-84628-569-1
eBook Packages: Springer Book Archive