Hostname: page-component-586b7cd67f-rdxmf Total loading time: 0 Render date: 2024-11-29T05:06:43.840Z Has data issue: false hasContentIssue false
  • English
  • Français

Some Results On The Asymptotic Behavior Of Linear Systems

Published online by Cambridge University Press:  20 November 2018

M. Marcus
M. Marcus*
Affiliation:
University of British Columbia
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

1. Introduction. We consider first in §2 the asymptotic behavior as t → ∞ of the solutions of the vector-matrix differential equation

(1.1) ,

where A is a constant n-square complex matrix, B{t) a continuous complex valued n-square matrix defined on [0, ∞ ), and x a complex n-vector.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 7 , 1955 , pp. 531 - 538
Copyright
Copyright © Canadian Mathematical Society 1955

References

1. Bellman, R., Stability theory of differential equations (New York, 1953).Google Scholar
2. Favard, J., Sur les équations différentielles linéaires à coefficients presque-périodiques, Acta Mathematica, 51 (1927), 31–81.Google Scholar
3. Gronwall, T. H., Note on the derivatives with respect to a parameter of the solutions of a system of differential equations, Annals of Math., 20 (1918), 292–296.Google Scholar
4. Zubov, V. I., Some sufficient criteria for stability of a non-linear system of differential equations, Akad. Nauk. SSSR. Prikl. Mat. Meh. 17 (1953), 506-508; Math. Rev., 15 (1954), 126 Google Scholar