IJPAM: Volume 34, No. 4 (2007)

UNIFORMLY AND ASYMPTOTIC STABILITY FOR TIME
VARYING DYNAMIC SYSTEM WITH LINEAR PART
ON TIME SCALES

I.B. Ya$\d s$ar$^1$, M.T. Dastjerdi$^2$
$^1$Department of Mathematics
Faculty of Sciences and Arts
University of Gazi
Be$\d s$evler, Ankara, 06500, TURKEY
e-mail: irfany@gazi.edu.tr
$^2$Department of Mathematics
Faculty of Sciences
Unevirsity of Zanjan
Zanjan, 45195-313, IRAN
e-mail: tdast@yahoo.com


Abstract.In this article by using the Lyapunov criteria, we study conditions that the solutions of a time varying dynamic system with linear part of the form ${x}^{\Delta}=A(t)x(t)+F(t,x(t))$ remain stable on certain time scales.

Received: August 27, 2006

AMS Subject Classification: 37N35, 93D20

Key Words and Phrases: uniformly stability, exponential stability, time scales, Lyapunov system, dynamic system

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2007
Volume: 34
Issue: 4