Lipschitz stability of impulsive systems of differential equations

1993 ◽  
Vol 8 (1) ◽  
pp. 1-17 ◽  
Author(s):  
G. K. Kulev ◽  
D. D. Bainov
Keyword(s):  
Differential Equations ◽  
Lipschitz Stability ◽  
Impulsive Systems ◽  
Systems Of Differential Equations

scholarly journals On eventual stability of impulsive systems of differential equations

2001 ◽  
Vol 27 (8) ◽  
pp. 485-494
Author(s):  
A. A. Soliman
Keyword(s):  
Differential Equations ◽  
Lipschitz Stability ◽  
Impulsive Systems ◽  
Systems Of Differential Equations ◽  
Eventual Stability

The notions of Lipschitz stability of impulsive systems of differential equations are extended and the notions of eventual stability are introduced. New notions called eventual and eventual Lipschitz stability. We give some criteria and results.

scholarly journals Cone valued Lyapunov functions and Lipschitz stability of nonlinear systems of differential equations

1996 ◽  
Vol 19 (3) ◽  
pp. 435-440
Author(s):  
Olusola Akinyele
Keyword(s):  
Stability Analysis ◽  
Nonlinear Systems ◽  
Differential Equations ◽  
Lyapunov Functions ◽  
Practical Stability ◽  
Lipschitz Stability ◽  
Comparison Result ◽  
Systems Of Differential Equations ◽  
New Concepts ◽  
Perturbed Systems

We introduce a new comparison result which will be an important tool when we apply cone valued Lyapunov like functions. We also introduce new concepts ofϕ0-uniform Lipschitz stability and(λ,λ,ϕ0)-practical stability and employ our comparison result to carry out stability analysis of nonlinear systems. Our results are also applicable to nonlinear perturbed systems.

scholarly journals Averaging method and two-sided bounded solutions on the axis of systems with impulsive effects at non-fixed times

2021 ◽  
Vol 104 (4) ◽  
pp. 142-150
Author(s):  
O.N. Stanzhytskyi ◽  
◽  
A.T. Assanova ◽  
M.A. Mukash ◽  
◽  
...  
Keyword(s):  
Differential Equations ◽  
Averaging Method ◽  
Nonlinear Dynamical Systems ◽  
Asymptotic Properties ◽  
Stable Solution ◽  
Impulsive Systems ◽  
Nonlinear Dynamical ◽  
Systems Of Differential Equations ◽  
Averaged Systems ◽  
Fixed Times

The averaging method, originally offered by Krylov and Bogolyubov for ordinary differential equations, is one of the most widespread and effective methods for the analysis of nonlinear dynamical systems. Further, the averaging method was developed and applied for investigating of various problems. Impulsive systems of differential equations supply as mathematical models of objects that, during their evolution, they are subjected to the action of short-term forces. Many researches have been devoted to non-fixed impulse problems. For these problems, the existence, stability, and other asymptotic properties of solutions were studied and boundary value problems for impulsive systems were considered. Questions of the existence of periodic and almost periodic solutions to impulsive systems also were examined. In this paper, the averaging method is used to study the existence of two-sided solutions bounding on the axis of impulse systems of differential equations with non-fixed times. It is shown that a one-sided, bounding, asymptotically stable solution to the averaged system generates a two-sided solution to the exact system. The closeness of the corresponding solutions of the exact and averaged systems both on finite and infinite time intervals is substantiated by the first and second theorems of N.N. Bogolyubov.

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