We introduce and solve the non-commutative version of Hermite-Pad\'{e} type I approximation problem. Its solution, expressed by quasideterminants, leads in a natural way to subclass solutions Hirota (discrete Kadomtsev--Petviashvili) system its linear also prove integrability constrained system, which simplest case is discrete-time Toda lattice equation known from theory Pad\'{e} approximants m...

Linear time-invariant time-delay systems (LTI-TDS) constitute a widespread family of plants and systems, not only limited to industrial ones. They can be represented by Laplace transfer functions in the form of fractions of so-called quasipolynomials. Direct controller design for LTI-TDS based on such models is mostly rather intricate. Many approaches require a rational approximation of the tra...

A reduced order modeling method based on a system description in terms of orthonormal Laguerre functions, together with a Krylov subspace decomposition technique is presented. The link with Padé approximation, the block Arnoldi process and singular value decomposition (SVD) leads to a simple and stable implementation of the algorithm. Novel features of the approach include the determination of ...

We improve the class of indices for which normality takes place in a Nikishin system and apply this in Hermite-Padé approximation of such systems of functions.

A standard approach to reduced-order modeling of higher-order linear dynamical systems is to rewrite the system as an equivalent first-order system and then employ Krylov-subspace techniques for reduced-order modeling of first-order systems. While this approach results in reduced-order models that are characterized as Padé-type or even true Padé approximants of the system’s transfer function, i...