Uniform asymptotic stability of impulsively perturbed nonlinear differential equations

1980 ◽  
Vol 4 (3) ◽  
pp. 599-606
Author(s):  
M. Rama Mohana Rao ◽  
V. Sree Hari Rao
Keyword(s):  
Asymptotic Stability ◽  
Differential Equations ◽  
Nonlinear Differential Equations ◽  
Uniform Asymptotic Stability

scholarly journals Asymptotic behavior of a class of perturbed differential equations

2021 ◽  
Vol 73 (5) ◽  
pp. 627-639
Author(s):  
A. Dorgham ◽  
M. Hammi ◽  
M. A. Hammami
Keyword(s):  
Asymptotic Behavior ◽  
Asymptotic Stability ◽  
Differential Equations ◽  
Integral Inequality ◽  
Nonlinear Differential Equations ◽  
Sufficient Conditions ◽  
Uniform Asymptotic Stability ◽  
Small Ball ◽  
Theoretical Results

UDC 517.9 This paper deals with the problem of stability of nonlinear differential equations with perturbations. Sufficient conditions for global uniform asymptotic stability in terms of Lyapunov-like functions and integral inequality are obtained. The asymptotic behavior is studied in the sense that the trajectories converge to a small ball centered at the origin. Furthermore, an illustrative example in the plane is given to verify the effectiveness of the theoretical results.    

Nonlinear Differential Equations and Feedback Control Design for the Urban–Rural Resident Pension Insurance in China

2015 ◽  
Vol 25 (14) ◽  
pp. 1540029
Author(s):  
Lijian Wang
Keyword(s):  
Asymptotic Stability ◽  
Differential Equations ◽  
Nonlinear Differential Equations ◽  
Control Design ◽  
Rural Resident ◽  
Pension Insurance ◽  
Modern Control Theory ◽  
Insurance System ◽  
Urban Rural ◽  
Pension Insurance System

Facing many problems of the urban–rural resident pension insurance system in China, one should firstly make sure that this system can be optimized. This paper, based on the modern control theory, sets up differential equations as models to describe the urban–rural resident pension insurance system, and discusses the globally asymptotic stability in the sense of Liapunov for the urban–rural resident pension insurance system in the new equilibrium point. This research sets the stage for our further discussion, and it is theoretically important and convenient for optimizing the urban–rural resident pension insurance system.

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