Stabilization of Equations with Delays

Abstract

In this chapter, we consider equations with delays. Namely, the derivative of an unknown function at a certain time depends on the values of the function at previous times. More exactly, we consider in the model aftereffect phenomena by adding a memory term. Engineers conclude that actuators, sensors that are involved in feedback control, introduce, in addition, delays into the system. That is why from the control engineering point of view it is of great interest to consider control problems associated with equations with delays. Furthermore, special kinds of substances, such as viscoelastic fluids, may also impose such delays. We will prove here that the proportional feedback, designed in Chap. 2, still ensures stability for this kind of system.