Extended Horizon Liftings for Periodic Gain Adjustments in Control Systems, and for Equalization of Communication Channels

Periodic gain adjustment in plants of irreducible order, n, or for equalization of communications channels is effected in such a way that the plant (system) appears to be minimum phase by choosing a horizon time N greater then n of liftings in periodic input and output windows Pu and Py, respectively, where N is an integer chosen to define the extent (length) of each of the windows Pu and Py, and n is the order of an irreducible input/output plant. The plant may be an electrical, mechanical or chemical system, in which case output tracking (OT) is carried out for feedback control or a communication channel, in which case input tracking (IT) is carried out. Conditions for OT are distinct from IT in terms of zero annihilation, namely for OT and of IT, where the OT conditions are intended for gain adjustments in the control system, and IT conditions are intended for equalization for communication channels.