Asymptotic properties of neutral type linear systems

TL;DR

This paper investigates the exponential stability and solution estimates of neutral type linear systems with time-varying coefficients and delays, providing explicit bounds valid for both short and long-term behaviors.

Contribution

It introduces new explicit exponential estimates for solutions of neutral systems, applicable to a broad class of systems with time-varying parameters and delays.

Findings

Derived explicit exponential bounds for solutions

Established stability tests for neutral systems with delays

Provided estimates valid on finite segments

Abstract

Exponential stability and solution estimates are investigated for a delay system $$ \dot{x}(t) - A(t)\dot{x}(g(t))=\sum_{k=1}^m B_k(t)x(h_k(t)) $$ of a neutral type, where $A$ and $B_k$ are $n\times n$ 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 behaviour of solutions.