On a generalized flat input definition and physical realizability

We generalize the definition of flat inputs to implicit nonlinear differential equations of order α > 1. By allowing injections of input components and its time derivatives up to some finite order δ in both the dynamics and the output equations we show that physical realizability of generalized flat inputs can be achieved in cases that were shown to possess no physically realizable flat input. In addition, it can be shown that there always exists a physically realizable (generalized) flat input of order δ < α in the linear case.