@article{KUCERA1998263,
    Abstract = {Motivated by the pole placement design techniques, linear polynomial (or diophantine) equations have become a popular design tool of control engineers. The paper presents the theory, properties, and computational algorithms for the equation ax + by = c in a tutorial manner. Recent results are presented on the parametrization of limited degreee solutions, of relatively prime solutions, and of solutions x, y such that y/x is proper rational. Parametric and non-parametric computational algorithms are discussed in detail. R{\'e}sum{\'e} Motiv{\'e}es par les m{\'e}thodes de placement des p{\^o}les, les {\'e}quations lin{\'e}aires polynomiales (ou Diophantine) sont de venue un outil math{\'e}matique polulaire parmi les automaticiens. Cette communication a pour but de pr{\'e}senter, d'une mani{\`e}re synoptique, la th{\'e}orie et le calcul num{\'e}rique li{\'e}s {\`a} l' {\'e}quation ax + by = c. Plusieurs r{\'e}sultats r{\'e}cents sont pr{\'e}sent{\'e}s, sur la param{\'e}trisation des solutions x, y de degr{\'e} born{\'e}, sur les solutions x, y premi{\`e}res entre elles et sur les solutions telles que le rapport y/x est rationnel et propre. Plusieurs m{\'e}thodes de r{\'e}solution de cette {\'e}quation, param{\'e}triques ou non, sont discut{\'e}es en d{\'e}tail.},
    Author = {Ku{\v c}era, V.},
    File = {Polynomial Equations - A Tool for Control Systems Synthesis - 1-s2.0-S1474667017420027-main - a - o.pdf},
    ISSN = {1474-6670},
    Journal = {IFAC Proceedings Volumes},
    Keywords = {Linear control systems, pole assignment, polynomial methods, parametrization, numerical solutions, software tools},
    Note = {5th IFAC Conference on System Structure and Control 1998 (SSC'98), Nantes, France, 8-10 July},
    Number = {18},
    Pages = {263 - 268},
    Title = {Polynomial Equations: A Tool for Control Systems Synthesis},
    URL = {http://www.sciencedirect.com/science/article/pii/S1474667017420027},
    Volume = {31},
    Year = {1998},
    bdsk-url-1 = {http://www.sciencedirect.com/science/article/pii/S1474667017420027},
    bdsk-url-2 = {https://doi.org/10.1016/S1474-6670(17)42002-7},
    date-added = {2020-10-16 16:40:33 +0200},
    date-modified = {2020-10-16 16:40:33 +0200},
    doi = {10.1016/S1474-6670(17)42002-7}
}

@article{KUCERA1998263, Abstract = {Motivated by the pole placement design techniques, linear polynomial (or diophantine) equations have become a popular design tool of control engineers. The paper presents the theory, properties, and computational algorithms for the equation ax + by = c in a tutorial manner. Recent results are presented on the parametrization of limited degreee solutions, of relatively prime solutions, and of solutions x, y such that y/x is proper rational. Parametric and non-parametric computational algorithms are discussed in detail. R{\'e}sum{\'e} Motiv{\'e}es par les m{\'e}thodes de placement des p{\^o}les, les {\'e}quations lin{\'e}aires polynomiales (ou Diophantine) sont de venue un outil math{\'e}matique polulaire parmi les automaticiens. Cette communication a pour but de pr{\'e}senter, d'une mani{`e}re synoptique, la th{\'e}orie et le calcul num{\'e}rique li{\'e}s {`a} l' {\'e}quation ax + by = c. Plusieurs r{\'e}sultats r{\'e}cents sont pr{\'e}sent{\'e}s, sur la param{\'e}trisation des solutions x, y de degr{\'e} born{\'e}, sur les solutions x, y premi{`e}res entre elles et sur les solutions telles que le rapport y/x est rationnel et propre. Plusieurs m{\'e}thodes de r{\'e}solution de cette {\'e}quation, param{\'e}triques ou non, sont discut{\'e}es en d{\'e}tail.}, Author = {Ku{\v c}era, V.}, File = {Polynomial Equations - A Tool for Control Systems Synthesis - 1-s2.0-S1474667017420027-main - a - o.pdf}, ISSN = {1474-6670}, Journal = {IFAC Proceedings Volumes}, Keywords = {Linear control systems, pole assignment, polynomial methods, parametrization, numerical solutions, software tools}, Note = {5th IFAC Conference on System Structure and Control 1998 (SSC'98), Nantes, France, 8-10 July}, Number = {18}, Pages = {263 - 268}, Title = {Polynomial Equations: A Tool for Control Systems Synthesis}, URL = {http://www.sciencedirect.com/science/article/pii/S1474667017420027}, Volume = {31}, Year = {1998}, bdsk-url-1 = {http://www.sciencedirect.com/science/article/pii/S1474667017420027}, bdsk-url-2 = {https://doi.org/10.1016/S1474-6670(17)42002-7}, date-added = {2020-10-16 16:40:33 +0200}, date-modified = {2020-10-16 16:40:33 +0200}, doi = {10.1016/S1474-6670(17)42002-7} }