Asymptotic properties of neutral type linear systems

Abstract

Exponential stability and solution estimates are investigated for a delay systemof 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.