Structured Noncommutative Multidimensional Linear Systems

Structured Noncommutative Multidimensional Linear Systems

We introduce a class of multidimensional linear systems with evolution along a free semigroup. The transfer function for such a system is a formal power series in noncommuting indeterminates. Standard system-theoretic properties (the operations of cascade/parallel connection and inversion, controllability, observability, Kalman decomposition, state-space similarity theorem, minimal state-space ...

Structured Noncommutative Multidimenisonal Linear Systems and Scale-Recursive Modeling

Recently, the multiscale signal and image processing community has recognized that a suitable model for multiresolution processes is a model with time-like variable indexed by the nodes on a homogeneous tree with different depths in the tree corresponding to different spatial scales associated with the signal or image. It turns out that these system models are close relatives of the Structured ...

Multidimensional structured matrices and polynomial systems

We apply and extend some well known and some recent techniques from algebraic residue theory in order to relate to each other two major subjects of algebraic and numerical computing that is computations with structured matrices and solving a system of polynomial equations In the rst part of our paper we extend the Toeplitz and Hankel structures of matrices and some of their known properties to ...

Relative parametrization of linear multidimensional systems

In the last chapter of his book ”The Algebraic Theory of Modular Systems ” published in 1916, F. S. Macaulay developped specific techniques for dealing with ”unmixed polynomial ideals ” by introducing what he called ”inverse systems ”. The purpose of this paper is to extend such a point of view to differential modules defined by linear multidimensional systems, that is by linear systems of ordi...

Multidimensional Linear Systems and Robust Control