Periodized characteristic equation and stability analysis of LTI systems with several delays*

The paper describes the construction of the periodized characteristic equation (PCE) for multivariable LTI systems with several delays. Then the asymptotic stability of the system is guaranteed, when all roots of the PCE are outside the unit circle, i.e. are located in the region |ζ| > 1. It is shown that practically always, the stability investigation can be traced back to studying the location of the roots of a certain polynomial with respect to the unit circle |ζ| = 1.