Proper deflating subspaces: Properties, algorithms and applications
Let \(\lambda M - N\) with \(M,N \in \mathbb{R}^{p \times q}\) be an arbitrary matrix pencil. The space \({\mathcal V}\), spanned by the columns \(V \in \mathbb{R}^{q \times r}\) is called a proper \(C_ 1\) deflating subspace if for some \(S \in \mathbb{R}^{r \times r}\), \(NV = MVS\) with \(MV\) of full column rank and the eigenvalues of \(S\) in \(C_ 1\). This paper describes an algorithm to compute such (maximal) deflating subspaces. It refines existing algorithms by an efficient combination of an algorithm for computing the generalized Schur form of the pencil and an algorithm for pole placement of linear systems given in descriptor form. The algorithm can also be used to compute a stabilizing solution of a generalized or constrained Riccati equation for continuous as well as discrete time. The latter application is also discussed in some detail.
scientific article; zbMATH DE number 640749
scientific article