On stability in nonlinear approximation of systems of impulsive differential equations

Theorems on existence of the Lyapunov functions for homogeneous systems of impulsive differential equations were proved. The results obtained were applied to studying stability in nonlinear approximation of the critical equilibria of the nonlinear systems of impulsive differential equations. An exam...

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Bibliographic Details
Published in:Automation and remote control 2014-11, Vol.75 (11), p.1893-1905
Main Authors: Dvirnyi, A. I., Slyn’ko, V. I.
Format: Article
Language:English
Subjects:
Approximation
CAE) and Design
Calculus of Variations and Optimal Control
Optimization
Computer-Aided Engineering (CAD
Control
Differential equations
Dynamical systems
Lyapunov functions
Mathematical analysis
Mathematics
Mathematics and Statistics
Mechanical Engineering
Mechatronics
Nonlinear Systems
Nonlinearity
Remote control
Robotics
Stability
Systems Theory
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Summary:Theorems on existence of the Lyapunov functions for homogeneous systems of impulsive differential equations were proved. The results obtained were applied to studying stability in nonlinear approximation of the critical equilibria of the nonlinear systems of impulsive differential equations. An example of a second-order system was given.
ISSN:0005-1179
1608-3032
DOI:10.1134/S0005117914110010