Matrix pencil of closed-loop descriptor systems: infinite-eigenvalue assignment

Abstract

The regular matrix pencil [sE – A – BK] is considered that characterizes a closed-loop descriptor system , u(t) = Kx(t) + ũ(t). A carefully contrived and efficient method is given for the determination of a set of matrices K such that the determinant ∣sE – A – BK∣ is a constant value independent of s. The problem is formulated as an infinite-eigenvalue assignment by finite-gain descriptor-variable feedback via a singular value decomposition of the matrix E. The result is interesting in its own right and finds application in controller and observer design.