Mismatching Problem between Generic Pole-assignabilities by Static Output Feedback and Dynamic Output Feedback in Linear Systems

In this paper, it is clearly shown that the two well-known necessary and sufficient conditions mp ≥ n as generic static output feedback pole-assignment and mp + d(m+p) ≥ n+d as generic minimum d-th order dynamic output feedback pole-assignment on complex field , unbelievably, do not match up each other in strictly proper linear systems. For the analysis, a diagram analysis is newly created (which is defined by the analysis of “convoluted rectangular/dot diagrams” constructed via node-branch conversion of the signal flow graphs of output feedback gain loops). Under this diagram analysis, it is proved that the minimum d-th order dynamic output feedback compensator for pole-assignment in m-input, p-output, n-th order systems is quantitatively decomposed into static output feedback compensator and its associated d number of arbitrary 1st order dynamic elements in augmented (m+d)-input, (p+d)-output, (n+d)-th order systems. Total configuration of the mismatched data is presented in a Table.