An approach for pole assignment by gain output feedback in square singular systems

This study deals with the problem of (finite) pole assignment in a linear, time-invariant, multivariable, singular system Ex = Ax -f Bu, with output y = Cx, via a gain output feedback of the form u = Ky + r that preserves the uniqueness property. It is shown that the problem of pole assignment in singular and regular systems are closely related from both analysis and synthesis points of view. The use of an appropriate transformation group enables one to apply the following approach: first to design a gain output feedback in a regular (rather than in a singular) system, and then to incorporate the output feedback into the original singular system while preserving the spectra obtained in the regular system. The present approach bridges the gap between the relevant theory in regular and singular systems, and simplifies the mechanism for the evaluation of a suitable gain output feedback in a given singular system.