Exponential stability of linear impulsive differential equations

1992 ◽  
Vol 31 (7) ◽  
pp. 1325-1334 ◽  
Author(s):  
N. V. Milev ◽  
D. D. Bainov
Keyword(s):  
Differential Equations ◽  
Exponential Stability ◽  
Impulsive Differential Equations

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 Stabilization of Stochastic Differential Equations Driven by G-Brownian Motion with Aperiodically Intermittent Control

Mathematics ◽  
2021 ◽  
Vol 9 (9) ◽  
pp. 988
Author(s):  
Pengju Duan
Keyword(s):  
Brownian Motion ◽  
Lyapunov Function ◽  
Differential Equations ◽  
Exponential Stability ◽  
Stochastic Differential Equations ◽  
Mild Solution ◽  
Intermittent Control

The paper is devoted to studying the exponential stability of a mild solution of stochastic differential equations driven by G-Brownian motion with an aperiodically intermittent control. The aperiodically intermittent control is added into the drift coefficients, when intermittent intervals and coefficients satisfy suitable conditions; by use of the G-Lyapunov function, the p-th exponential stability is obtained. Finally, an example is given to illustrate the availability of the obtained results.

Sign in / Sign up

Export Citation Format

Share Document