Reducing subspaces : computational aspects and applications in linear systems theory

The fixed poles of the disturbance decoupling problem and almost stability subspace $\mathcal V^\star_{b,g}({\rm ker}(C))$

“…Associated with the generalized upper triangular form (7), the following reducing subspaces have been studied in [7,8,[16][17][18].…”

“…We would like to thank the anonymous referee for the invaluable suggestions, comments and giving us the references [8,17,18].…”

“…The main results in [6] will be used to establish coordinate-free solvability conditions for the DDP and DDPM. It has been shown in [7,8,[16][17][18] that any specific reducing subspace can be computed by numerically stable methods. Hence, we link the DDP, DDPM and the associated fixed poles with the reducing subspace technique in numerical linear algebra.…”

“…There are two advantages to our approach. It is based on the well-established reducing subspace technique [7,8,[16][17][18] whose ingredients are orthogonal transformations which can be implemented as numerical stable algorithms, thus guaranteeing robust computation of the desired quantities, if this is possible. Therefore, our approach leads to numerically reliable algorithms to compute σ s and σ m .…”