On H∞ control for dead-time systems

A mixed sensitivity H∞ problem is solved for dead-time systems. It is shown that for a given bound on the H∞-norm there exist causal stabilizing controllers that achieve this bound if and only if a related finite-dimensional Riccati equation has a solution with a certain nonsingularity property. In the case of zero time-delay the Riccati equation is a standard Riccati equation and the nonsingularity condition is that the solution be nonnegative definite. For non-zero time-delay the non-singularity condition is more involved but still allows to obtain controllers. All sub-optimal controllers are parameterized and the central controller is shown to be a feedback interconnection of a finite dimensional system and a finite memory system, both of which can be implemented. Some H∞ problems are rewritten as pure rational H∞ problems using a Smith predictor parameterization of the controller.