Control of Linear Delay Systems: An Approach without Explicit Predictions

The control of linear time-invariant systems with incommensurate lumped and distributed delays is addressed. Using a module-theoretic point of view where these systems are modules over the ring of entire functions in ℝ(s)[e− τ s ] necessary and sufficient conditions for the freeness of these modules are presented. If these conditions hold a module basis can be used to design a tracking controller that assigns an arbitrary finite spectrum to the closed loop. Though the controller is infinite dimensional, in general, it does not involve any explicit predictions. This generalizes the so-called reduction approach, by which for certain state representations predictions can be calculated exactly and thus finite spectrum assignment can be achieved. Examples illustrate the main results.