Characteristic Equation for MIMO Linear Continuous Periodic Systems with Several Delays

The paper considers a multidimensional linear continuous system with periodic and delayed feedback. The several delays could be incommensurable to each other and to the period T. For this kind of systems a method for constructing the characteristic equation is provided. The approach is based on the parametric transfer matrix concept and the theory of Fredholm integral equations of the second kind. The relations between the characteristic equation and the stability behavior of the system are investigated. Finally some computational aspects are discussed.