Control of systems with I/O delay via reduction to a one-block problem

In this note, the standard (four-block) H-infinity control problem for systems with a single delay in the feedback loop is studied. A simple procedure of the reduction of the problem to an equivalent one-block problem having particularly simple structure is proposed. The one-block problem is then solved by the J-spectral factorization approach, resulting in the so-called dead-time compensator (DTC) form of the controller. The advantages of the proposed procedure are its simplicity, intuitively clear derivation of the DTC form of the H-infinity controller, and extensibility to the multiple delay case.