A simplified behavioral approach to inversion-based control of linear systems

For linear time-invariant systems, we introduce a simplified behavioral approach which is based on piecewise infinitely differentiable functions. Compared to the function space used in the standard behavioral approach, our setting allows to simplify mathematical machinery while at the same time preserving the richness of signal’s features required in many practical applications (e.g. mechatronics one). We employ the simplified behavioral approach to derive two main contributions to the field of inversion-based control. As a first contribution, we introduce a novel solution to the stable input-output inversion problem for square nonminimum-phase systems. Differently from state-of-the-art solutions, our solution can be applied to nondecoupable systems too. As a second contribution, we formally prove the equivalence among the two most common inversion architectures: the closed-loop and plant inversion architecture. This equivalence dictates that the two architectures deliver the same performances for any disturbance and mis-modeling affecting the controlled plant.