A Trajectory-Based Approach to Discrete-Time Flatness

For discrete-time systems, flatness is usually defined by replacing the time-derivatives of well-known continuous-time definition forward-shifts. With this definition, class flat systems corresponds exactly to which can be linearized a endogenous dynamic feedback as it proposed in literature. Recently, verifiable necessary and sufficient differential-geometric conditions for property have been derived. In present contribution, we make an attempt take into account also backward-shifts. This extended approach motivated one-to-one correspondence solutions trivial system known from case. If transfer idea case, leads allows To distinguish classical with forward-shifts paper, refer former forward-flatness. We show that (in sense backward-shifts) still share many beneficial properties forward-flat systems. particular, they are reachable/controllable, allow straightforward planning trajectories certain subclass feedbacks.