ABSTRACT
The concept of difference flatness, for discrete time systems, directly stems from the concept of differential flatness in continuous time systems. The fundamental property of flatness, in discrete time systems, is analogous to its continuous time counterpart: it allows for a complete difference parametrization of all system variables, including the inputs, in terms of a special set of independent variables, called the flat outputs. These artificial outputs exhibit the same cardinality as the set of control inputs. The flat outputs are difference functions of the state, i.e., they are functions of the state and of a finite number of advances of the state. This implies that the flat outputs are functions of the state and of a finite number of advances of the input variables. In discrete time systems, however, an alternative exists for the definition of the flat output also in terms of a function of the states and of a finite number of previous values of the state. Although both definitions are equivalent, the first one may encounter a lack causality problem in controller designs based on flatness, while the second definition does not.
