The Orbit Closure Problem for Matrix Pencils: Neccessary Conditions and an Application to High Gain Feedback

Abstract

For a given state space system ∑, which singular systems can occur as a limit ∑ of under high gain feedback? We identify linear systems with rectangular matrix pencils and view this question in terms of orbit closure under the strict equivalence action of GLp x GLq on the space of pxq matrix pencils. We determine necessary conditions for a singular system to be a limit of a given state space system under high gain feedback.