03372nam a22004815i 4500001001800000003000900018005001700027007001500044008004100059020003700100024002400137041000800161100003000169245010400199260006100303264006100364300003400425336002600459337002600485338003600511347002400547490007200571505094700643520082001590650001702410650002502427650002002452650001502472650001702487650002502504650004302529650002902572650002402601700003002625710003402655773002002689776003602709830007202745856003702817912001402854942000702868999001502875978-3-540-31594-0DE-He21320141014113512.0cr nn 008mamaa100806s2005 gw | s |||| 0|eng d a97835403159409978-3-540-31594-07 a10.1007/b969772doi aeng1 aHenrion, Didier.eeditor.10aPositive Polynomials in Controlh[electronic resource] /cedited by Didier Henrion, Andrea Garulli. 1aBerlin, Heidelberg :bSpringer Berlin Heidelberg,c2005. 1aBerlin, Heidelberg :bSpringer Berlin Heidelberg,c2005. aXII, 316 p.bonline resource. atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda1 aLecture Notes in Control and Information Science,x0170-8643 ;v3120 aFrom 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. aPositive 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. 0aEngineering. 0aGeometry, algebraic. 0aSystems theory. 0aVibration.14aEngineering.24aControl Engineering.24aVibration, Dynamical Systems, Control.24aSystems Theory, Control.24aAlgebraic Geometry.1 aGarulli, Andrea.eeditor.2 aSpringerLink (Online service)0 tSpringer eBooks08iPrinted edition:z9783540239482 0aLecture Notes in Control and Information Science,x0170-8643 ;v31240uhttp://dx.doi.org/10.1007/b96977 aZDB-2-ENG cEB c2786d2786