Preservation of the Exponential Stability under Perturbations of Linear Delay Impulsive Differential Equations

1995 ◽  
Vol 14 (1) ◽  
pp. 157-174 ◽  
Author(s):  
L. Berezansky ◽  
Elena Braverman
Keyword(s):  
Differential Equations ◽  
Exponential Stability ◽  
Impulsive Differential Equations ◽  
Linear Delay ◽  
Stability Under Perturbations

scholarly journals Stability analysis for $ (\omega, c) $-periodic non-instantaneous impulsive differential equations

2022 ◽  
Vol 7 (2) ◽  
pp. 1758-1774
Author(s):  
Kui Liu ◽  
Keyword(s):  
Stability Analysis ◽  
Differential Equations ◽  
Exponential Stability ◽  
Periodic Solutions ◽  
Sufficient Conditions ◽  
Impulsive Differential Equations ◽  
Cauchy Matrix ◽  
Impulsive Problems ◽  
The Stability ◽  
Homogeneous Linear

<abstract><p>In this paper, the stability of $ (\omega, c) $-periodic solutions of non-instantaneous impulses differential equations is studied. The exponential stability of homogeneous linear non-instantaneous impulsive problems is studied by using Cauchy matrix, and some sufficient conditions for exponential stability are obtained. Further, by using Gronwall inequality, sufficient conditions for exponential stability of $ (\omega, c) $-periodic solutions of nonlinear noninstantaneous impulsive problems are established. Finally, some examples are given to illustrate the correctness of the conclusion.</p></abstract>

scholarly journals New Stability Conditions for Linear Differential Equations with Several Delays

2011 ◽  
Vol 2011 ◽  
pp. 1-19 ◽  
Author(s):  
Leonid Berezansky ◽  
Elena Braverman
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Exponential Stability ◽  
Delay Differential Equation ◽  
Linear Differential Equations ◽  
Stability Conditions ◽  
Linear Delay ◽  
Linear Differential ◽  
Several Delays ◽  
Delay Differential

New explicit conditions of asymptotic and exponential stability are obtained for the scalar nonautonomous linear delay differential equationx˙(t)+∑k=1mak(t)x(hk(t))=0with measurable delays and coefficients. These results are compared to known stability tests.

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