Positive Polynomials in Control originates from an invited session presented at the IEEE CDC 2003 and gives a comprehensive overview of existing results in this quickly emerging area. This carefully edited book collects important contributions from several fields of control, optimization, and mathematics, in order to show different views and approaches of polynomial positivity. The book is organized in three parts, reflecting the current trends in the area: 1. applications of positive polynomials and LMI optimization to solve various control problems, 2. a mathematical overview of different…mehr
Positive Polynomials in Control originates from an invited session presented at the IEEE CDC 2003 and gives a comprehensive overview of existing results in this quickly emerging area. This carefully edited book collects important contributions from several fields of control, optimization, and mathematics, in order to show different views and approaches of polynomial positivity. The book is organized in three parts, reflecting the current trends in the area: 1. applications of positive polynomials and LMI optimization to solve various control problems, 2. a mathematical overview of different algebraic techniques used to cope with polynomial positivity, 3. numerical aspects of positivity of polynomials, and recently developed software tools which can be employed to solve the problems discussed in the book.
Produktdetails
Produktdetails
Lecture Notes in Control and Information Sciences 312
Artikelnr. des Verlages: 10997703, 978-3-540-23948-2
2005
Seitenzahl: 328
Erscheinungstermin: 14. Januar 2005
Englisch
Abmessung: 235mm x 155mm x 18mm
Gewicht: 496g
ISBN-13: 9783540239482
ISBN-10: 3540239480
Artikelnr.: 13919900
Autorenporträt
Didier Henrion, LAAS-CNRS, Toulouse, France / Andrea Garulli, Università di Siena, Siena, Italy
Inhaltsangabe
From the contents: Part I Control Applications of Polynomial Positivity Control Applications of Sum of Squares Programming; Analysis of Non-polynomial Systems Using the Sum of Squares Decomposition; A Sum-of-Squares Approach to Fixed-Order H8-Synthesis; LMI Optimization for Fixed-Order H8 Controller Design; An LMI-based Technique for Robust Stability Analysis of Linear Systems with Polynomial Parametric Uncertainties; Stabilization of LPV Systems.- Part II Algebraic Approaches to Polynomial Positivity on the Equivalence of Algebraic Approaches to the Minimization of Forms on the Simplex; Moment Approach to Analyze Zeros of Triangular Polynomial Sets; Polynomials Positive on Unbounded Rectangles; Stability of Interval Two-Variable Polynomials and Quasipolynomials via Positivity.- Part III Numerical Aspects of Polynomial Positivity: Structures, Algorithms, Software Tools Exploiting Algebraic Structure in Sum of Squares Programs.
From the contents: Part I Control Applications of Polynomial Positivity Control Applications of Sum of Squares Programming; Analysis of Non-polynomial Systems Using the Sum of Squares Decomposition; A Sum-of-Squares Approach to Fixed-Order H8-Synthesis; LMI Optimization for Fixed-Order H8 Controller Design; An LMI-based Technique for Robust Stability Analysis of Linear Systems with Polynomial Parametric Uncertainties; Stabilization of LPV Systems.- Part II Algebraic Approaches to Polynomial Positivity on the Equivalence of Algebraic Approaches to the Minimization of Forms on the Simplex; Moment Approach to Analyze Zeros of Triangular Polynomial Sets; Polynomials Positive on Unbounded Rectangles; Stability of Interval Two-Variable Polynomials and Quasipolynomials via Positivity.- Part III Numerical Aspects of Polynomial Positivity: Structures, Algorithms, Software Tools Exploiting Algebraic Structure in Sum of Squares Programs.
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