Abstract
We are concerned with the asymptotic stability of linear delay systems. Under the condition that parameter matrices of the systems have common eigenvectors, the stability analysis may be reduced to that of lower dimensional systems. A method for the analysis is presented by means of eigenpairs of the parameter matrices. Our results are illustrated by two examples.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
J. Bacuteelair, Stability in delayed neural networks. Ordinary and Delay Differential Equations (Eds. J. Wiener and J. Hale), Longman Scientific & Technical, New York, 1992, 6–9.
M. Barszcz and A. Olbert, Stability criterion for a linear differential-difference systems. IEEE Trans. Automat. Control.,2 (1979), 368–369.
M. Buslowicz, Simple stability criterion for a class of delay differential systems. Internat. J. Systems Sci.,5 (1987), 993–995.
K. Gopalsamy, Stability and Oscillations in Delay Differential Equations of Population Dynamics. Kluwer Academic Publishers, Dordrecht, 1992.
R. Horn and C. Johnson, Matrix Analysis. Cambridge University Press, 1985.
T. Mori and E. Noldus, Stability criteria for linear differential difference systems. Internat. J. Systems Sci.,1 (1984), 87–94.
V.V. Prasolov, Problems and Theorems in Linear Algebra. Amer. Math. Soc., 1994.
Author information
Authors and Affiliations
Corresponding author
About this article
Cite this article
Hu, GD., Mitsui, T. Stability of linear delay differential systems with matrices having common eigenvectors. Japan J. Indust. Appl. Math. 13, 487–494 (1996). https://doi.org/10.1007/BF03167259
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF03167259