Exponential Stability of Dynamic Systems on Time Scales

2013 ◽  
pp. 55-62
Author(s):  
Zbigniew Bartosiewicz ◽  
Ewa Piotrowska ◽  
Alan S. I. Zinober
Keyword(s):  
Exponential Stability ◽  
Time Scales ◽  
Dynamic Systems

scholarly journals -Exponential Stability of Nonlinear Impulsive Dynamic Equations on Time Scales

2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Author(s):  
Veysel Fuat Hatipoğlu ◽  
Deniz Uçar ◽  
Zeynep Fidan Koçak
Keyword(s):  
Exponential Stability ◽  
Time Scales ◽  
Dynamic Systems ◽  
Global Exponential Stability ◽  
Dynamic Equations ◽  
Stability Conditions

The purpose of this paper is to present the sufficient -exponential, uniform exponential, and global exponential stability conditions for nonlinear impulsive dynamic systems on time scales.

scholarly journals Lyapunov stability theory for dynamic systems on time scales

1992 ◽  
Vol 5 (3) ◽  
pp. 275-281 ◽  
Author(s):  
Billur Kaymakçalan
Keyword(s):  
Time Scales ◽  
Lyapunov Stability ◽  
Comparison Principle ◽  
Dynamic Systems ◽  
Stability Theory ◽  
Lyapunov Stability Theory ◽  
Existence Theory ◽  
Lyapunov’S Second Method ◽  
Stability Results

By use of the necessary calculus and the fundamental existence theory for dynamic systems on time scales, in this paper, we develop Lyapunov's second method in the framework of general comparison principle so that one can cover and include several stability results for both types of equations at the same time.

scholarly journals Stability analysis in terms of two measures for dynamic systems on time scales

1993 ◽  
Vol 6 (4) ◽  
pp. 325-344 ◽  
Author(s):  
Billûr Kaymakçalan
Keyword(s):  
Stability Analysis ◽  
Time Scales ◽  
Dynamic Systems ◽  
Lyapunov’S Second Method ◽  
Two Measures ◽  
Set Up ◽  
Stability Results ◽  
Stability Concepts ◽  
Single Set

Using the theory of Lyapunov's second method developed earlier for time scales, we extend our stability results to two measures which give rise to unification of several stability concepts in a single set up.

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