The fundamental subspace sequences of matrix pencils: A Toeplitz matrix unified characterization
The authors introduce an alternative theoretical method for calculating the fundamental sequences of the matrix pencil \((F,G)\). These fundamental sequences are, for instance, with the right choice for \(F\) and \(G\), the elements that appear in the controllability subspace algorithm. The advantage of studying the fundamental sequences lies in the fact that one covers subspace algorithms for implicit and proper systems at the same time. These sequences of subspaces are characterized via a partition of the right null spaces of certain Toeplitz matrices. These Toeplitz matrices contain only blocks that are zero, \(F\) or \(G\), and thus are very simple to build out of the system data. Although this approach to the fundamental sequence is purely theoretical, the authors have good hope that it will be useful for (numerical) computation as well.
scientific article; zbMATH DE number 1236302
scientific article