On H-infinity control for dead-time systems

A mixed sensitivity H-infinity problem is solved for dead-time systems. It is shown that for a given bound on the H-infinity-norm causal stabilizing c ontrollers exist that achieve this bound if and only if a related finite-di mensional Riccati equation has a solution with a certain nonsingularity pro perty. In the case of zero time delay, the Riccati equation is a standard R iccati equation and the nonsingularity condition is that the solution be no nnegative definite, For nonzero time delay, the nonsingularity condition is more involved but still allows us to obtain controllers. All suboptimal co ntrollers are parameterized, and the central controller is shown to be a fe edback interconnection of a finite-dimensional system and a finite memory s ystem, both of which can be implemented, Some H-infinity problems are rewri tten as pure rational H-infinity problems using a Smith predictor parameter ization of the controller.