Descriptor Systems Under Feedback and Output Injection

Abstract

In this paper we study simultaneous feedback and output injection on descriptor linear system described by a quadruple of matrices (E,A,B,C). We describe the possible Kronecker invariants of the resulting pencil λE−(A+ BF + KC), when F and K vary, in the case when the pencil corresponding to the system (E,A,B,C) has no infinite elementary divisors of the second, third and fourth type. The solution is constructive and explicit, and is given over algebraically closed fields.