On some testable conditions for excitability and transparency of a class of time-delay systems with point delays

This article is concerned with the excitability of positive linear time-invariant systems subject to internal point delays. It is proved that the excitability independent of delay is guaranteed if an auxiliary delay-free system is excitable. Necessary and sufficient conditions for excitability and transparency are formulated in terms of the parameterization of the dynamics and control matrices and, equivalently, in terms of strict positivity of a matrix of an associate system obtained from the influence graph of the original system. Such conditions are testable through simple algebraic tests involving moderate computational effort.