An Approach for Pole Assignment in Singular Systems

An approach for pole assignment in a singular system Ex = Ax + Bu is developed. It is shown that the problem of assigning the roots of det (sE — (A + BF)) by applying a proportional feedback u = Fx + r in a given singular system is equivalent to the problem of pole assignment in an appropriate regular system. An immediate application of the presented approach is that procedures and computational algorithms that were originally developed for assigning eigenvalues in regular systems become useful tools for pole assignment in singular systems. The present approach provides a useful tool with regard to the combined problem of eliminating impulsive behavior and stabilizing a singular system.