Closing the Loop in Moment Matching
Alessio Moreschini, Alessandro Astolfi · 2024
We present a novel closed-loop interpretation of the steady-state notion of moment. In particular, to close the loop in an interconnection-based moment-matching configuration we introduce a signal generator that ensures internal stability of the interconnection while interpolating the moments of the underlying system. Unlike the traditional open-loop configuration, the closed-loop scheme allows the relaxation of the internal stability property of the underlying system. Furthermore, for a fixed signal generator, we provide conditions for any linear models to achieve moment matching in closed loop. In particular, we define the family of all (stable and unstable) admissible plants achieving moment matching through the same signal generator. These results offer a new perspective on moment matching and yield a moment matching interpretation of the dual Youla-Kučera parameterization.