scholarly journals Vector Lyapunov functions for practical stability of nonlinear impulsive functional differential equations

2007 ◽  
Vol 325 (1) ◽  
pp. 612-623 ◽  
Author(s):  
Ivanka M. Stamova
Keyword(s):  
Differential Equations ◽  
Lyapunov Functions ◽  
Functional Differential Equations ◽  
Practical Stability ◽  
Vector Lyapunov Functions ◽  
Functional Differential

Uniform practical stability in terms of two measures with effect of delay at the time of impulses

2016 ◽  
Vol 0 (0) ◽  
Author(s):  
Palwinder Singh ◽  
Sanjay K. Srivastava ◽  
Kanwalpreet Kaur
Keyword(s):  
Differential Equations ◽  
Lyapunov Functions ◽  
Functional Differential Equations ◽  
Sufficient Conditions ◽  
Practical Stability ◽  
Two Measures ◽  
Piecewise Continuous ◽  
Functional Differential

AbstractIn this paper, some sufficient conditions for uniform practical stability of impulsive functional differential equations in terms of two measures with effect of delay at the time of impulses are obtained by using piecewise continuous Lyapunov functions and Razumikhin techniques. The application of obtained result is illustrated with an example.

scholarly journals Practical Stability with Respect to h-Manifolds for Impulsive Control Functional Differential Equations with Variable Impulsive Perturbations

Mathematics ◽  
2019 ◽  
Vol 7 (7) ◽  
pp. 656 ◽  
Author(s):  
Gani Stamov ◽  
Ivanka Stamova ◽  
Xiaodi Li ◽  
Ekaterina Gospodinova
Keyword(s):  
Differential Equations ◽  
Impulsive Control ◽  
Functional Differential Equations ◽  
Cellular Neural Network ◽  
Continuous Functions ◽  
Practical Stability ◽  
Piecewise Continuous ◽  
Impulsive Perturbations ◽  
Functional Differential ◽  
Control Functional

The present paper is devoted to the problems of practical stability with respect to h-manifolds for impulsive control differential equations with variable impulsive perturbations. We will consider these problems in light of the Lyapunov–Razumikhin method of piecewise continuous functions. The new results are applied to an impulsive control cellular neural network model with variable impulsive perturbations.

scholarly journals New Results on Impulsive Functional Differential Equations with Infinite Delays

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Jie Yang ◽  
Bing Xie
Keyword(s):  
Differential Equations ◽  
Lyapunov Functions ◽  
Functional Differential Equations ◽  
Stability Behavior ◽  
Razumikhin Technique ◽  
Infinite Delays ◽  
Functional Differential ◽  
The Stability

We investigate the stability for a class of impulsive functional differential equations with infinite delays by using Lyapunov functions and Razumikhin-technique. Some new Razumikhin-type theorems on stability are obtained, which shows that impulses do contribute to the system’s stability behavior. An example is also given to illustrate the importance of our results.

scholarly journals Stability of the solutions of impulsive functional-differential equations by Lyapunov's direct method

2001 ◽  
Vol 43 (2) ◽  
pp. 269-278 ◽  
Author(s):  
D. D. Bainov ◽  
I. M. Stamova
Keyword(s):  
Differential Equations ◽  
Lyapunov Functions ◽  
Direct Method ◽  
Functional Differential Equations ◽  
Sufficient Conditions ◽  
Zero Solution ◽  
Continuous Functions ◽  
Piecewise Continuous ◽  
Functional Differential ◽  
The Stability

AbstractWe consider the stability of the zero solution of a system of impulsive functional-differential equations. By means of piecewise continuous functions, which are generalizations of classical Lyapunov functions, and using a technique due to Razumikhin, sufficient conditions are found for stability, uniform stability and asymptotical stability of the zero solution of these equations. Applications to impulsive population dynamics are also discussed.

scholarly journals LaSalle-Type Theorems for General Nonlinear Stochastic Functional Differential Equations by Multiple Lyapunov Functions

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Xueyan Zhao ◽  
Feiqi Deng ◽  
Xiaojing Zhong
Keyword(s):  
Differential Equations ◽  
Lyapunov Functions ◽  
Functional Differential Equations ◽  
Stochastic Functional Differential Equations ◽  
Multiple Lyapunov Functions ◽  
Functional Differential ◽  
Derivatives Of ◽  
Special Case ◽  
Stochastic Functional

We investigate LaSalle-type theorems for general nonlinear stochastic functional differential equations. With some preliminaries on lemmas and the derivation techniques, we establish three LaSalle-type theorems for the general nonlinear stochastic functional differential equations via multiple Lyapunov functions. For the typical special case with estimations involving|xt|pfor the derivatives of the Lyapunov functions, a theorem is established as the corollary of the main theorem. At the end of the paper, an example is given to illustrate the usage of the method proposed and show the advantage of the results obtained.

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