Abstract
This lecture will deal with the application of the methods and spirit of modern algebra [LANG, 1965] to the theory of linear dynamical systems. We shall be concerned mainly with the following topics:
-
(i)
the representation of linear systems;
-
(ii)
the problem of realization;
-
(iii)
duality.
Supported in part by the U.S. Air Force under Contract 49 (638)-1440.
This is a preview of subscription content, log in via an institution to check access.
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
Arbib, M. A., [1965] A common framework for automata theory and control theory. SIAM J. Control, 3, pp. 206–222.
Ho, B. L.; Kalman, R. E., [1966] Effective construction of linear state-variable models from input/output functions. Proc. Third Allerton Conference, pp. 449-459; Regelungstechnik, 14, pp. 545-548.
Kalman, R. E., [1960 A] Contributions to the theory of optimal control. Bol. Soc. Mat. Mexicana, 5, pp. 102–119.
Kalman, R. E., [1960B] On the general theory of control systems. Proc. 1st IFAC Congress, Moscow; Butterworths, London.
Kalman, R. E., [1965] Algebraic structure of linear dynamical systems. I. The module of Z. Proc. Nat. Acad. Sci. (USA), 54, pp. 1503–1508.
Kalman, R. E., [1967] Algebraic aspects of the theory of dynamical systems, in Differential Equations and Dynamical Systems. J. K. Hale and J. P. LaSalle (eds.), pp. 133-146, Academic Press.
Kalman, R. E., [1969] Lectures on Algebraic System Theory, Springer Lecture Notes in Mathematics (to appear).
Kalman, R. E.; Falb, P. L.; Arbib, M. A., [1968] Topics in Mathematical System Theory. McGraw-Hill.
Krohn, K. B.; Rhodes, J. L., [1965] Algebraic theory of machines. I. The main decomposition theorem. Trans. Am. Math. Soc., 116, pp. 450–464.
Lang, S., [1965] Algebra. Addison-Wesley.
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1969 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Kalman, R.E. (1969). Introduction to the Algebraic Theory of Linear Dynamical Systems. In: Kuhn, H.W., Szegö, G.P. (eds) Mathematical Systems Theory and Economics I / II. Lecture Notes in Operations Research and Mathematical Economics, vol 11/12. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-46196-5_4
Download citation
DOI: https://doi.org/10.1007/978-3-642-46196-5_4
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-04635-6
Online ISBN: 978-3-642-46196-5
eBook Packages: Springer Book Archive