Asymptotic properties of neutral type linear systems

2020/12/21 by Berezansky, Leonid, Braverman, Elena
#34K06 #34K20 #34K25 #34K40 #Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.2012.11507

Abstract

Exponential stability and solution estimates are investigated for a delay system x(t) - A(t)x(g(t))=∑_k=1^m B_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 behaviour of solutions.

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