Characteristic equation and stability analysis of linear periodic systems with delay

For a linear continuous periodic system with several delays, a characteristic equation is defined in such a way, that for its stability it is necessary and sufficient that all its roots are outside the closed unit disc. By applying the theory of Fredholm integral equations of the second kind, an approximate characteristic equation is derived in polynomial form. Conditions are given, under which the exact and the approximate equation yield the same stability statement. An example illustrates how this method could be applied.