Asymptotic properties of neutral type linear systems

Leonid Berezansky; Elena Braverman

doi:10.1016/j.jmaa.2020.124893

Asymptotic properties of neutral type linear systems

Leonid Berezansky, Elena Braverman

Department of Mathematics

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

6 Scopus citations

Abstract

Exponential stability and solution estimates are investigated for a delay system x˙(t)−A(t)x˙(g(t))=∑k=1mB_k(t)x(h_k(t)) of a neutral type, where A and B_k are n×n bounded matrix functions, and g,h_k are delayed arguments. Stability tests are applicable to a wide class of linear neutral systems with time-varying coefficients and delays. In addition, explicit exponential estimates for solutions of both homogeneous and non-homogeneous neutral systems are obtained for the first time. These inequalities are not just asymptotic estimates, they are valid on every finite segment and evaluate both short- and long-term behavior of solutions.

Original language	English
Article number	124893
Journal	Journal of Mathematical Analysis and Applications
Volume	497
Issue number	2
DOIs	https://doi.org/10.1016/j.jmaa.2020.124893
State	Published - 15 May 2021

Keywords

Exponential estimates of solutions
Exponential stability
Linear neutral delay system
Matrix measure
Non-autonomous system

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.1016/j.jmaa.2020.124893

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title = "Asymptotic properties of neutral type linear systems",

abstract = "Exponential stability and solution estimates are investigated for a delay system x˙(t)−A(t)x˙(g(t))=∑k=1mBk(t)x(hk(t)) of a neutral type, where A and Bk are n×n bounded matrix functions, and g,hk are delayed arguments. Stability tests are applicable to a wide class of linear neutral systems with time-varying coefficients and delays. In addition, explicit exponential estimates for solutions of both homogeneous and non-homogeneous neutral systems are obtained for the first time. These inequalities are not just asymptotic estimates, they are valid on every finite segment and evaluate both short- and long-term behavior of solutions.",

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AU - Braverman, Elena

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N2 - Exponential stability and solution estimates are investigated for a delay system x˙(t)−A(t)x˙(g(t))=∑k=1mBk(t)x(hk(t)) of a neutral type, where A and Bk are n×n bounded matrix functions, and g,hk are delayed arguments. Stability tests are applicable to a wide class of linear neutral systems with time-varying coefficients and delays. In addition, explicit exponential estimates for solutions of both homogeneous and non-homogeneous neutral systems are obtained for the first time. These inequalities are not just asymptotic estimates, they are valid on every finite segment and evaluate both short- and long-term behavior of solutions.

AB - Exponential stability and solution estimates are investigated for a delay system x˙(t)−A(t)x˙(g(t))=∑k=1mBk(t)x(hk(t)) of a neutral type, where A and Bk are n×n bounded matrix functions, and g,hk are delayed arguments. Stability tests are applicable to a wide class of linear neutral systems with time-varying coefficients and delays. In addition, explicit exponential estimates for solutions of both homogeneous and non-homogeneous neutral systems are obtained for the first time. These inequalities are not just asymptotic estimates, they are valid on every finite segment and evaluate both short- and long-term behavior of solutions.

KW - Exponential estimates of solutions

KW - Exponential stability

KW - Linear neutral delay system

KW - Matrix measure

KW - Non-autonomous system

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Asymptotic properties of neutral type linear systems

Abstract

Keywords

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