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Effective algorithms for parametrizing linear control systems over Ore algebras
TLDR
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
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OreModules: A Symbolic Package for the Study of Multidimensional Linear Systems
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]. InExpand
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On a General Structure of the Stabilizing Controllers Based on Stable Range
  • A. Quadrat
  • Computer Science, Mathematics
  • SIAM J. Control. Optim.
  • 1 June 2003
TLDR
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
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Applications of the Quillen-Suslin theorem to multidimensional systems theory
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 asExpand
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On a generalization of the Youla–Kučera parametrization. Part II: the lattice approach to MIMO systems
  • A. Quadrat
  • Mathematics, Computer Science
  • Math. Control. Signals Syst.
  • 1 August 2006
TLDR
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
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The Fractional Representation Approach to Synthesis Problems: An Algebraic Analysis Viewpoint Part II: Internal Stabilization
  • A. Quadrat
  • Mathematics, Computer Science
  • SIAM J. Control. Optim.
  • 2003
TLDR
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
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Computation of bases of free modules over the Weyl algebras
TLDR
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
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Generalized Bezout Identity
  • J. Pommaret, A. Quadrat
  • Mathematics, Computer Science
  • Applicable Algebra in Engineering, Communication…
  • 1 July 1998
TLDR
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
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Factoring and decomposing a class of linear functional systems
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
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On a generalization of the Youla-Kučera parametrization. Part I: the fractional ideal approach to SISO systems
  • A. Quadrat
  • Mathematics, Computer Science
  • Syst. Control. Lett.
  • 7 October 2003
TLDR
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
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