Method of Lyapunov functions in problems of stability of solutions of systems of differential equations with impulse action

2003 ◽  
Vol 194 (10) ◽  
pp. 1543-1558 ◽  
Author(s):  
A O Ignat'yev
Keyword(s):  
Differential Equations ◽  
Lyapunov Functions ◽  
Stability Of Solutions ◽  
Impulse Action ◽  
Systems Of Differential Equations

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 Stability of Perturbed Set Differential Equations Involving Causal Operators in Regard to Their Unperturbed Ones considering Difference in Initial Conditions

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Coșkun Yakar ◽  
Hazm Talab
Keyword(s):  
Differential Equations ◽  
Lyapunov Functions ◽  
Initial Conditions ◽  
Lyapunov Functionals ◽  
Stability Of Solutions ◽  
Causal Operators ◽  
The Difference ◽  
The Stability

We investigate the stability of solutions of perturbed set differential equations with causal operators in regard to their corresponding unperturbed ones considering the difference in initial conditions (time and position) by utilizing Lyapunov functions and Lyapunov functionals.

Lyapunov functions and a control problem

1967 ◽  
Vol 63 (2) ◽  
pp. 435-438 ◽  
Author(s):  
A. A. Kayande ◽  
D. B. Muley
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Control Problem ◽  
Lyapunov Functions ◽  
Differential Inequality ◽  
Differential Systems ◽  
Systems Of Differential Equations ◽  
Linear Differential Systems ◽  
Lyapunov’S Second Method ◽  
Linear Differential

1. One of the most important techniques in the study of non-linear differential systems is the Lyapunov's second method and its extensions. One of the extensions of the method depends upon the fact that the function satisfying a differential inequality can be majorized by the maximal solution of the corresponding differential equation. This method was used extensively by V. Lakshmikantham and others for obtaining results, in a unified way, on stability and boundedness of systems of differential equations.

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