Strong Structural Non-Minimum Phase Systems

Structural analysis can reveal properties of the investigated systems without knowing the exact parameters of the system, for example masses, geometries or resistor values. Properties that can be determined are for instance controllability and observability. Recently, there have been investigations about structural stability and structural non-minimum phase behavior. In general by considering the structure of a system a precise answer if the mentioned properties hold numerically can not be given. This led to the introduction of strong structural properties, that hold for all admissible numerically realization of the analyzed system. In this paper the strong structural non-minimum phase property is investigated. The representation of a dynamical system as a graph is proposed for the structural analysis. A method to calculate the invariant zeros polynomial from the graph-theoretic representation of a square MIMO systems is introduced. From that method the strong structural non-minimum phase property is derived. An example for the application of the method is given.