Stable transformations for control variable delayed systems

A well-known transformation containing a transport-type integral induces a feedback controller for control variable delayed systems. More recent numerical simulations, based on the discretization of the transport-type integral, have cast doubt on the stabilizing property of this controller. Further investigation has revealed that the null space of the transport-type integral is a potential source of a destabilizing input for the closed-loop system; this is the hidden input problem. On the basis of the concept of a stable transformation, a new feedback stabilizing controller is formulated to address the hidden input problem. An additional benefit of the stable transformation theory is a quasi-functional observer which allows the new feedback controller to be implemented as a constant multiple of an augmented state variable.