Exponential stability of systems of vector delay differential equations with applications to second order equations

Leonid Berezansky; Elena Braverman

doi:10.1016/j.jmaa.2021.125566

Exponential stability of systems of vector delay differential equations with applications to second order equations

Leonid Berezansky, Elena Braverman

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

Abstract

Various results and techniques, such as the Bohl-Perron theorem, a priori estimates of solutions, M-matrices and the matrix measure, are applied to obtain new explicit exponential stability conditions for the system of vector functional differential equations x˙_i(t)=A_i(t)x_i(h_i(t))+∑j=1n∑k=1m_ijB_ij^k(t)x_j(h_ij^k(t))+∑j=1n∫g_ij(t)tK_ij(t,s)x_j(s)ds,i=1,…,n. Here x_i are unknown vector-functions, A_i,B_ij^k,K_ij are matrix functions, h_i,h_ij^k,g_ij are delayed arguments. Using these results, we deduce explicit exponential stability tests for second order vector delay differential equations.

Original language	English
Article number	125566
Journal	Journal of Mathematical Analysis and Applications
Volume	504
Issue number	2
DOIs	https://doi.org/10.1016/j.jmaa.2021.125566
State	Published - 15 Dec 2021

Keywords

Bohl-Perron theorem
Differential systems with matrix coefficients and a distributed delay
Exponential stability
M-matrices
Matrix measure
Second order vector delay differential equations

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.1016/j.jmaa.2021.125566

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title = "Exponential stability of systems of vector delay differential equations with applications to second order equations",

abstract = "Various results and techniques, such as the Bohl-Perron theorem, a priori estimates of solutions, M-matrices and the matrix measure, are applied to obtain new explicit exponential stability conditions for the system of vector functional differential equations x˙i(t)=Ai(t)xi(hi(t))+∑j=1n∑k=1mijBijk(t)xj(hijk(t))+∑j=1n∫gij(t)tKij(t,s)xj(s)ds,i=1,…,n. Here xi are unknown vector-functions, Ai,Bijk,Kij are matrix functions, hi,hijk,gij are delayed arguments. Using these results, we deduce explicit exponential stability tests for second order vector delay differential equations.",

keywords = "Bohl-Perron theorem, Differential systems with matrix coefficients and a distributed delay, Exponential stability, M-matrices, Matrix measure, Second order vector delay differential equations",

author = "Leonid Berezansky and Elena Braverman",

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AU - Braverman, Elena

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N2 - Various results and techniques, such as the Bohl-Perron theorem, a priori estimates of solutions, M-matrices and the matrix measure, are applied to obtain new explicit exponential stability conditions for the system of vector functional differential equations x˙i(t)=Ai(t)xi(hi(t))+∑j=1n∑k=1mijBijk(t)xj(hijk(t))+∑j=1n∫gij(t)tKij(t,s)xj(s)ds,i=1,…,n. Here xi are unknown vector-functions, Ai,Bijk,Kij are matrix functions, hi,hijk,gij are delayed arguments. Using these results, we deduce explicit exponential stability tests for second order vector delay differential equations.

AB - Various results and techniques, such as the Bohl-Perron theorem, a priori estimates of solutions, M-matrices and the matrix measure, are applied to obtain new explicit exponential stability conditions for the system of vector functional differential equations x˙i(t)=Ai(t)xi(hi(t))+∑j=1n∑k=1mijBijk(t)xj(hijk(t))+∑j=1n∫gij(t)tKij(t,s)xj(s)ds,i=1,…,n. Here xi are unknown vector-functions, Ai,Bijk,Kij are matrix functions, hi,hijk,gij are delayed arguments. Using these results, we deduce explicit exponential stability tests for second order vector delay differential equations.

KW - Bohl-Perron theorem

KW - Differential systems with matrix coefficients and a distributed delay

KW - Exponential stability

KW - M-matrices

KW - Matrix measure

KW - Second order vector delay differential equations

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Exponential stability of systems of vector delay differential equations with applications to second order equations

Abstract

Keywords

ASJC Scopus subject areas

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