A graph-oriented approach to address generically flat outputs in structured LTI discrete-time systems
Taha Boukhobza (Lorraine University)
Jacob van der Woude (TU Delft - Mathematical Physics)
Christian Commault (Université Grenoble Alpes)
Gilles Millérioux (Lorraine University)
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Abstract
This paper addresses difference flatness for structured LTI discrete-time systems. Two forms of necessary and sufficient conditions for an output to be a structural flat output are given. First, a preliminary result algebraically defines a flat output in terms of invariant zeros regardless whether an LTI system is structured or not. Next, the conditions are expressed in terms of graphical conditions to define a structural flat output. Checking for the graphical conditions calls for algorithms that have polynomial-time complexity and that are commonly used for digraphs. The tractability of the conditions is illustrated on several examples.