LAUSR

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 behavior of solutions.