A note on the differential regulator equation for non-minimum phase linear systems with time-varying exosystems

Some control problems in practice are often formulated as a linear output regulation problem with time-varying exosystems. Although this problem has been studied recently, an explicit and constructive solution has been given only for minimum phase systems. This paper presents a solution for non-minimum phase systems whose zero dynamics is hyperbolic (or has an exponentially dichotomic split in the case of time-varying zero dynamics). The idea is inspired by the non-causal stable inversion.