On the Linearization of Flat Multi-Input Systems via Prolongations

Abstract: We examine when differentially flat nonlinear control systems with more than two inputs can be rendered static feedback linearizable by prolongations of suitably chosen inputs after applying a static input transformation. Building on the structure of the time derivatives of a flat output, we derive sufficient conditions that guarantee such prolongations yield a static feedback linearizable system. In the two-input case, prior work established precise links between relative degrees, the highest derivative orders occurring in a flat parameterization, and the minimal dimension of a linearizing dynamic extension, leading to necessary and sufficient criteria for systems that become static feedback linearizable after at most two prolongations of such suitably chosen inputs. This work extends this analysis to systems with more than two inputs and derives particular results for the three-input case.