Delay-interval stability and hyperbolicity of linear time-delay systems: A matrix pencil approach

This paper focuses on the problems of asymptotic stability and hyperbolicity for a class of linear systems described by delay differential equations with commensurable delays. Delay-interval necessary and sufficient conditions are given in terms of eigenvalues distribution with respect to the unit circle of two constant and regular matrix pencils: one associated to finite time-delays and the other one associated to infinite delay. The so-called "delay-independent" and "delay-dependent" cases are also considered. Furthermore. a second order example from the literature is completely treated.