Abstract
Let us consider a linear dynamical system
where A: X→X, B: U→X are bounded linear operators, X (the state space) and U (the control or input space) are some normed linear spaces.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Васюнин, В.И.; Никольский, H.К.: Управляющие подпространства минимальной размерности. Элементарное введение. Discotheca, Записки научн. семинаров ЛОМИ, Ленинград, 113(1981), 41–75.
Васюнин, В.И.; Никольский, Н.К.: Управляющие подпространства минимальной размерности. Влияние корневых векторов. Discotheca, Препринт ЛОМИ, P-4-81,Ленинград, 1981, 1-45.
Васюнин, В.И.; Никольский, Н.К.: Управляющие подпространства минимальной размерности. Унитарные и модельные операторы. Discotheca, Препринт ЛОМИ, P-5-81, Ленинград, 1981.
Никольский, H.К.: Лекции об операторе сдвига, Москва, “Наука”, 1980.
Feintuch, A: On single input controllability for infinite dimensional linear systems, J. Math. Anal. Appl. 62 (1978), 538–546.
Heymann, M.: On the input and output reducibility of multivariable linear systems, IEEE Trans. Aut. Control AC-15(1970), 563–569.
Sarason, D.: Weak-star density of polynomials, J. Reine Angew. Math. 252 (1972), 1–15.
Wermer, J.: On invariant subspaces of normal operators, Proc. Amer. Math. Soc. 3 (1952), 270–277.
Wermer, J.: On restrictions of operators, Proc. Amer. Math. Soc. 4 (1953), 860–865.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1982 Springer Basel AG
About this chapter
Cite this chapter
Nikolskii, N.K., Vasjunin, V.I. (1982). Control Subspaces of Minimal Dimension, and Spectral Multiplicities. In: Apostol, C., Douglas, R.G., Sz.-Nagy, B., Voiculescu, D., Arsene, G. (eds) Invariant Subspaces and Other Topics. Operator Theory: Advances and Applications, vol 6. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-5445-0_13
Download citation
DOI: https://doi.org/10.1007/978-3-0348-5445-0_13
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-5447-4
Online ISBN: 978-3-0348-5445-0
eBook Packages: Springer Book Archive