Symbolic Methods for Solving Algebraic Systems of Equations and Applications for Testing the Structural Stability

DOI10.1007/978-3-030-38356-5_8zbMath1448.93052OpenAlexW3029000689MaRDI QIDQ5118408

Yacine Bouzidi, Fabrice Rouillier

Publication date: 8 September 2020

Published in: Algebraic and Symbolic Computation Methods in Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://hal.inria.fr/hal-02907338/file/chapitre_springer.pdf

zbMATH Keywords

structural stabilitymultidimensional systemsalgebraic systemssymbolic methodsreal solvingcertified computations

Mathematics Subject Classification ID

Multivariable systems, multidimensional control systems (93C35) Lyapunov and other classical stabilities (Lagrange, Poisson, (L^p, l^p), etc.) in control theory (93D05) Linear systems in control theory (93C05) Algebraic methods (93B25)

Uses Software

• MPFI
• ISOLATE

Cites Work

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• Subdivision methods for solving polynomial equations
• Solving zero-dimensional systems through the rational univariate representation
• A new efficient algorithm for computing Gröbner bases \((F_4)\)
• Efficient isolation of polynomial's real roots.
• A pure power product version of the Hilbert Nullstellensatz
• Real solving for positive dimensional systems.
• Motivations for an arbitrary precision interval arithmetic and the MPFI library
• The DMM bound
• Multivariable Nyquist theory
• Introduction to Numerical Analysis
• Stability and stabilisation of linear multidimensional discrete systems in the frequency domain
• Algorithms in real algebraic geometry

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