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The existence and exponential stability of periodic solution for impulsive delay differential equations
Author(s) -
Lin Yusen,
Pu Xiaoqin,
Li Dingshi
Publication year - 2020
Publication title -
asian journal of control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.769
H-Index - 53
eISSN - 1934-6093
pISSN - 1561-8625
DOI - 10.1002/asjc.2076
Subject(s) - mathematics , exponential stability , fixed point theorem , banach fixed point theorem , stability (learning theory) , range (aeronautics) , exponential function , differential equation , fixed point , banach space , inequality , differential (mechanical device) , mathematical analysis , control theory (sociology) , computer science , nonlinear system , engineering , aerospace engineering , physics , materials science , control (management) , quantum mechanics , machine learning , artificial intelligence , composite material
In this work, we first establish a new generalized Halanay inequality with impulses, which have two advantages: one is that impulses can be applied to stabilize the unstable continuous system, the other is that the requirements on the coefficients of inequality are more relaxed than those in previous works. Then, by using the inequality and Banach fixed point theorem, we will obtain some sufficient conditions ensuring the existence and exponential stability of periodic solution for impulsive delay differential equations. The sufficient conditions are easily checked in practice and have a wider adaptive range. Some examples are given to illustrate our results.