We give effective algorithms which check whether or not a linear control system over some Ore algebra is controllable, parametrizable, flat or π-free.Expand

In the seventies, the study of transfer matrices of time-invariant linear systems of ordinary differential equations (ODEs) led to the development of the polynomial approach [20, 22, 44]. In… Expand

We prove that some stabilizing controllers of a plant, which admits a left/right-coprime factorization, have a special form where their stable and unstable parts are separated.Expand

The purpose of this paper is to give four new applications of the Quillen-Suslin theorem to mathematical systems theory. Using a constructive version of the Quillen-Suslin theorem, also known as… Expand

We obtain a general parametrization of all stabilizing controllers for internally stabilizable multi input multi output (MIMO) plants which do not necessarily admit doubly coprime factorizations.Expand

A portable cooking appliance comprising a heating device mounted in an oven having a structure consisting of at least one base, side and rear walls and a top portion associated with an external hot-plate.Expand

A well-known result due to J. T. Stafford asserts that a stably free left module $M$ over the Weyl algebras $D=A_n(k)$ or $B_n$ $-$ with $rank_D(M) \geq2$ is free.Expand

We show that the generalized Bezout identity is equivalent to the splitting of an exact differential sequence formed by the control system and its parametrization.Expand

Abstract Within a constructive homological algebra approach, we study the factorization and decomposition problems for a class of linear functional (determined, over-determined, under-determined)… Expand

We show how to generalize the Youla–Kucera parametrization of the stabilizing controllers to any stabilizable plant which does not necessarily admit a coprime factorization.Expand