The fixed poles of the disturbance decoupling problem and almost stability subspace ν* b,g (ker(C))

Abstract

This paper is concerned with the fixed poles of the disturbance decoupling problem for linear time-invariant systems by state feedback and measurement feedback. Algebraic characterizations for these fixed poles are given using the reducing subspace technique in numerical linear algebra. These algebraic characterizations lead that the fixed poles can be directly computed by numerically reliable algorithms. As an additional application of the reducing subspace technique, we also develop a numerically stable method for computing the almost stability subspace ν* b,g (ker(C)), which is an extension of the method given by Van Dooren for computing the invariant subspaces in geometric control theory.