Parameterisation of Degenerate Solutions of the Determinantal Assignment Problem

Abstract

The paper is concerned with defining and parametrising the families of all degenerate compensators (feedback, squaring down etc) emerging in a variety of linear control problems. Such compensators indicate the boundaries of the control design, but they also provide the means for linearising the non-linear nature of the Determinantal Assignment Problems, which provide the unifying description for all frequency assignment problems (pole, zero) under static and dynamic compensation schemes. The conditions provide the means for the selection of appropriate degenerate solutions that allow frequency assignability in the corresponding frequencies.