A note on the stability of habituating process control

For a class of single-output processes with at least two control inputs, this note proposes a simple control design and study its stability. To this end, the process is factorized into a stable and non-minimum-phase factor and a possible unstable minimum-phase factor. By the addition of a (low-pass) filter of suitable dimension, one can obtain a process factorization where the minimum-phase factor has a proper and stable inverse. Once the plant has been factorized in this form, the proposed control synthesis method is composed of two main steps; namely, output regulation based on the non-minimum-phase factor and design of an optimizationbased divider to compute the value corresponding to the multiple inputs. In this way, one obtains the control transfer function of each control input in a parallel control architecture. An analysis of the control structure is provided, giving sufficient conditions for the stability of the control loop.