Stabilization in the Presence of an Uncertain Arbitrarily Large Delay

Handling delays in control systems is difficult and is of long-standing interest. It is well known that, given a finite-dimensional linear time-invariant (LTI) plant and a finite-dimensional LTI stabilizing controller, closed-loop stability will be maintained under a small delay in the feedback loop. However, in some situations there is a large delay, perhaps arising from a slow communications link or a large but variable computational delay (e.g., in a system which uses image processing). While there are techniques available to design a controller to handle a known delay, there is no general theory for designing a controller to handle an arbitrarily large uncertain delay. Here we prove constructively that, given a finite-dimensional LTI plant and an upper bound on the admissible time delay, there exists a linear periodic controller which robustly stabilizes the plant.