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IEEE/CAA Journal of Automatica Sinica

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Laura Menini, Corrado Possieri and Antonio Tornambè, "Algorithms to Compute the Largest Invariant Set Contained in an Algebraic Set for Continuous-Time and Discrete-Time Nonlinear Systems," IEEE/CAA J. Autom. Sinica, vol. 7, no. 1, pp. 57-69, Jan. 2020. doi: 10.1109/JAS.2019.1911819
Citation: Laura Menini, Corrado Possieri and Antonio Tornambè, "Algorithms to Compute the Largest Invariant Set Contained in an Algebraic Set for Continuous-Time and Discrete-Time Nonlinear Systems," IEEE/CAA J. Autom. Sinica, vol. 7, no. 1, pp. 57-69, Jan. 2020. doi: 10.1109/JAS.2019.1911819

Algorithms to Compute the Largest Invariant Set Contained in an Algebraic Set for Continuous-Time and Discrete-Time Nonlinear Systems

doi: 10.1109/JAS.2019.1911819
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  • In this paper, some computational tools are proposed to determine the largest invariant set, with respect to either a continuous-time or a discrete-time system, that is contained in an algebraic set. In particular, it is shown that if the vector field governing the dynamics of the system is polynomial and the considered analytic set is a variety, then algorithms from algebraic geometry can be used to solve the considered problem. Examples of applications of the method (spanning from the characterization of the stability to the computation of the zero dynamics) are given all throughout the paper.

     

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    Highlights

    • Computational tools are proposed to determine the largest invariant set, with respect to either a continuous-time or a discrete-time system, that is contained in an algebraic set.
    • If the vector field governing the dynamics of the system is polynomial and the considered analytic set is a variety, then algorithms from algebraic geometry can be used to solve the considered problem.
    • Examples of applications of the method, spanning from the characterization of the stability to the computation of the zero dynamics, are given throughout the paper.

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