Necessary conditions for exponential stability of linear neutral type systems with multiple time delays

In this paper, we will give necessary conditions for the exponential stability of linear neutral type systems with multiple time delays by employing the Lyapunov-Krasovskii functional approach. These conditions not only extend the existing results of the neutral-delay-free systems, but also provide a new tool for stability analysis of linear neutral type systems with multiple time delays by characterizing instability domains. As a medium step, we will investigate several crucial properties which are involved with both the fundamental matrix and Lyapunov matrix. Numerical examples illustrate the validity of the theoretical results.