Perfectly robust deadbeat controller for systems with unknown delays

An explicit formula is presented for a perfectly robust deadbeat minimum time controller for a first order plant with unknown time delay. The controller has a remarkable property of robust stability and zero steady-state error for any perturbation of the time delay in the plant transfer function. This property is paradoxical in the sense that it never occurs for PID and other traditional controllers. Indeed, when we try to achieve the zero steady-state with the help of a traditional integration in the loop transfer function we automatically lose all chances to achieve robust stability for arbitrary delay perturbations due to infinite zero frequency gain