On the excitability of a class of positive continuous time-delay systems

This article is on the excitability of positive linear time-invariant systems subject to internal point delays. It is proved that excitability independent of delay is guaranteed if an auxiliary delay-free system is excitable. Necessary and sufficient conditions for excitability and transparency independent of the delay size are formulated in terms of the parameterization of the dynamics and control matrices. Some particular results are also given for the properties being dependent on the size of the point delay and for any possible finite values of the delay. The same formulation is given in parallel in terms of strict positivity of a matrix of an associate system obtained from the influence graph of the original system. The excitability and transparency properties are both testable through simple algebraic tests involving a moderate computational effort that is directly related to the system's order.