Asymptotic behaviour of real two-dimensional differential system with a finite number of constant delays

• Autorzy: Rebenda J.
• Języki publikacji: EN

Abstrakty

EN

In this article stability and asymptotic properties of a real two-dimensional system x'(t) = A(t)x(t) +[...]=i Bj(t)x(t - r j) + h(t, x (t), x (t - n), ...,x(t- rn)) are studied, where r1 > 0,..., rn > 0 are constant delays, A, B1, ..., Bn are the matrix functions and h is the vector function. Generalization of results on stability of a two-dimensional differential system with one constant delay is obtained using the methods of complexification and Lyapunov-Krasovskii functional and some new corollaries and an example are presented.

Słowa kluczowe

EN

Lyapunov method; stability; differential system

PL

metoda Lyapunova; opóźnienia stałe; system różniczkowy

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2008
• Tom: Vol. 41, nr 4
• Strony: 845--857
• Opis fizyczny: Bibliogr. 3 poz.

Twórcy

autor

Rebenda J.

• Department of Mathematics and Statistics Masaryk University Janackovo nam 2a 662 95 Brno, Czech Republik,

Bibliografia

• [1] J. Kalas, L. Barakova, Stability and asymptotic behaviour of a two-dimensional differential system with delay, J. Math. Anal. Appl. 269 (2002), 278-300.
• [2] M. Rab, J. Kalas, Stability of dynamical systems in the plane, Differential Integral Equations 3 (1990), 124-144.
• [3] J. Rebenda, Asymptotic properties of solutions of real two-dimensional differential systems with a finite number of constant delays, Mem. Differential Equations Math. Phys. 41 (2007), 97-114.