Effective algorithms for parametrizing linear control systems over Ore algebras

Linear Control Systems over Ore Algebras: Effective Algorithms for the Computation of Parametrizations

In this paper, we study linear control systems over Ore algebras. Within this mathematical framework, we can simultaneously deal with different classes of linear control systems such as time-varying ordinary differential systems, differential time-delay systems, partial differential equations, multidimensional discrete systems, etc. We give effective algorithms which check whether or not a line...

Effective algebraic analysis approach to linear systems over Ore algebras

Exact linear modeling using Ore algebras

Linear exact modeling is a problem coming from system identification: Given a set of observed trajectories, the goal is find a model (usually, a system of partial differential and/or difference equations) that explains the data as precisely as possible. The case of operators with constant coefficients is well studied and known in the systems theoretic literature, whereas the operators with vary...

Algorithms for solving linear systems over cyclotomic fields

We consider the problem of solving a linear system Ax = b over a cyclotomic field. What makes cyclotomic fields of special interest is that we can easily find a prime p that splits the minimal polynomial m(z) for the field into linear factors. This makes it possible to develop very fast modular algorithms. We give two output sensitive modular algorithms, one using multiple primes and Chinese re...

Parametrizing All Solutions of Uncontrollable Multidimensional Linear Systems

Using an algebraic analysis approach, we derive a necessary and sufficient condition so that we can parametrize all solutions of a multidimensional linear system by glueing the controllable sub-behaviour with the autonomous elements. Effective algorithms checking this condition are obtained. This result generalizes a result of 1-D linear systems for a class of multidimensional linear systems. C...