Stability and hyperbolicity of linear time-delay systems: A matrix pencil tensor product approach

This note focuses on the stability and hyperbolicity problems for a class of linear systems described by delay-differential equations including commensurable delays. An unitary approach is proposed via a matrix pencil technique using some 'special' Kronecker products and sums. Necessary and sufficient conditions, delay-independent or delay-dependent, are given in terms of the generalized eigenvalues distribution of two constant and regular matrix pencils associated to finite and infinite delays, respectively. The proposed approach recover results from the literature (Niculescu, 1996; Niculescu et al., 1996), by reducing the dimension of the involved matrix pencils. Copyright (C) 1998 IFAC.