Asymptotic properties of neutral type linear systems

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.

16 pages, no figures. Accepted to Journal of Mathematical Analysis and Applications