Constructing flat inputs for two-output systems

International audience ; In this paper, we study the problem of constructing flat inputs for two-output dynamical systems. The notion of flat inputs has been introduced by Waldherr and Zeitz [2008, 2010] and can be seen as dual to that of flat outputs. In the single-output case, a flat input can be constructed if and only if the original system together with its output is observable. In the multi-output case, the observability is not necessary for the existence of flat inputs. We start by discussing the case when the dynamical system together with the given output is observable and we present a generalization of the results of Waldherr and Zeitz [2010] by relating them with the notion of minimal differential weight. Then, we give our main theorems. We consider the unobservable case for which we study the local and global problems. We completely describe the local case, discuss the issue of the minimal modification of the original system, and propose a solution for the global problem. Finally, we explain how our results can be applied to secure communication.