Every stabilizing dead-time controller has an observer-predictor-based structure

This paper considers the stabilization problem for linear time-invariant (LTI) systems with a single delay h in the feedback loop. Two parametrizations of all stabilizing controllers are derived in terms of a state-space realization of the rational part of the plant. These parametrizations have simple structures and clear interpretations: the first is in the form of a generalized dead-time compensator (Smith predictor) and the second is in the observer-predictor form. Applications of the proposed parametrization to the H optimization and the robust stabilization problems are discussed.