@article{HARMS2017677,
    Abstract = {Consider a nonlinear input-affine control system x(t) = f(x(t)) + g(x(t))u(t), y(t) = h(x(t)), where f, g, h are polynomial functions. Let S be a set given by algebraic equations and inequations (in the sense of =). Such sets appear, for instance, in the theory of the Thomas decomposition, which is used to write a variety as a disjoint union of simpler subsets. The set S is called controlled invariant if there exists a polynomial state feedback law u(t) = {$\alpha$}(x(t)) such that S is an invariant set of the closed loop system x = (f + g{$\alpha$})(x). If it is possible to achieve this goal with a polynomial output feedback law u(t) = {$\beta$}(y(t)), then S is called controlled and conditioned invariant. These properties are discussed and algebraically characterized, and algorithms are provided for checking them with symbolic computation methods.},
    Author = {Harms, Melanie and Schilli, Christian and Zerz, Eva},
    File = {Polynomial Control Systems - Invariant Sets given by Algebraic EquationsInequations - 1-s2.0-S2405896317301532-main.pdf},
    ISSN = {2405-8963},
    Journal = {IFAC-PapersOnLine},
    Keywords = {Nonlinear control systems, Multivariable polynomials, Invariance, State feedback, Output feedback, Algebraic systems theory, Computational methods},
    Note = {20th IFAC World Congress},
    Number = {1},
    Pages = {677-680},
    Title = {Polynomial Control Systems: Invariant Sets given by Algebraic Equations/Inequations},
    URL = {https://www.sciencedirect.com/science/article/pii/S2405896317301532},
    Volume = {50},
    Year = {2017},
    bdsk-url-1 = {https://www.sciencedirect.com/science/article/pii/S2405896317301532},
    bdsk-url-2 = {https://doi.org/10.1016/j.ifacol.2017.08.118},
    date-added = {2023-02-21 20:51:55 +0100},
    date-modified = {2023-02-21 20:51:55 +0100},
    doi = {10.1016/j.ifacol.2017.08.118}
}

@article{HARMS2017677, Abstract = {Consider a nonlinear input-affine control system x(t) = f(x(t)) + g(x(t))u(t), y(t) = h(x(t)), where f, g, h are polynomial functions. Let S be a set given by algebraic equations and inequations (in the sense of =). Such sets appear, for instance, in the theory of the Thomas decomposition, which is used to write a variety as a disjoint union of simpler subsets. The set S is called controlled invariant if there exists a polynomial state feedback law u(t) = {$\alpha$}(x(t)) such that S is an invariant set of the closed loop system x = (f + g{$\alpha$})(x). If it is possible to achieve this goal with a polynomial output feedback law u(t) = {$\beta$}(y(t)), then S is called controlled and conditioned invariant. These properties are discussed and algebraically characterized, and algorithms are provided for checking them with symbolic computation methods.}, Author = {Harms, Melanie and Schilli, Christian and Zerz, Eva}, File = {Polynomial Control Systems - Invariant Sets given by Algebraic EquationsInequations - 1-s2.0-S2405896317301532-main.pdf}, ISSN = {2405-8963}, Journal = {IFAC-PapersOnLine}, Keywords = {Nonlinear control systems, Multivariable polynomials, Invariance, State feedback, Output feedback, Algebraic systems theory, Computational methods}, Note = {20th IFAC World Congress}, Number = {1}, Pages = {677-680}, Title = {Polynomial Control Systems: Invariant Sets given by Algebraic Equations/Inequations}, URL = {https://www.sciencedirect.com/science/article/pii/S2405896317301532}, Volume = {50}, Year = {2017}, bdsk-url-1 = {https://www.sciencedirect.com/science/article/pii/S2405896317301532}, bdsk-url-2 = {https://doi.org/10.1016/j.ifacol.2017.08.118}, date-added = {2023-02-21 20:51:55 +0100}, date-modified = {2023-02-21 20:51:55 +0100}, doi = {10.1016/j.ifacol.2017.08.118} }