A discussion of stability analysis for systems of differential equations with multiple and distributed delays

被引：0
作者：
Ioannis Dassios
Muyang Liu
Federico Milano
机构：
[1] University College Dublin,
[2] Xinjiang University,undefined
来源：
International Journal of Dynamics and Control | 2024年 / 12卷
关键词：
Delay differential equations; Systems; Multiple delays; Distributed; Numerical methods;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
In this article, we consider a class of systems of multiple delay differential equations (MDDEs). We first define a characteristic matrix equation that can be used to analyze the stability of the equilibrium of a system of MDDEs. Then we construct a matrix based on the coefficients of the characteristic matrix equation and use the spectrum of this matrix to derive necessary and sufficient conditions for the system to be stable. Next we discuss a comparison of the stability equivalency between a system of delay differential equations (DDEs) to the system of MDDEs and relate our results to distributed delay systems (DDSs). Numerical examples are given to justify our theory.
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页码：1279 / 1286
页数：7
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[1]  
Abolpour R(2021)Stability analysis of linear time-invariant systems in the presence of polytopic uncertainty and a time delay state Int J Dyn Control 9 945-956
[2]  
Fu P(2006)Stability of linear neutral time-delay systems: exact conditions via matrix pencil solutions IEEE Trans Autom Control 51 1063-3300
[3]  
Niculescu SI(2010)Krylov method for the delay eigenvalue problem SIAM J Sci Comput 21 3278-1653
[4]  
Chen J(2010)A Krylov method for the delay eigenvalue problem SIAM J Sci Comput 32 3278-227
[5]  
Jarlebring E(2019)On the stability analysis of systems of neutral delay differential equations Circuits Syst Signal Process 38 1639-653
[6]  
Meerbergen K(2022)On the relations between a singular system of differential equations and a system with delays Math Modell Numer Simul Appl 2 221-440
[7]  
Michiels WA(2022)The role of fear in a time-variant prey-predator model with multiple delays and alternative food source to predator Int J Dyn Control 10 630-3266
[8]  
Jarlebring E(2023)Asymptotic stability and linear feedback control of real order systems with multiple time delays Int J Dyn Control 11 428-117
[9]  
Meerbergen K(2016)Small-signal stability analysis of large power systems with inclusion of multiple delays IEEE Trans Power Syst 31 3257-24
[10]  
Michiels W(2011)Mean square exponential stability analysis of impulsive stochastic switched systems with mixed delays Comput Math Appl 62 109-636
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