Positive Polynomials in Control [electronic resource] / edited by Didier Henrion, Andrea Garulli.Material type: TextLanguage: English Series: Lecture Notes in Control and Information Science: 312Publisher: Berlin, Heidelberg : Springer Berlin Heidelberg, 2005Description: XII, 316 p. online resourceContent type: text Media type: computer Carrier type: online resourceISBN: 9783540315940Subject(s): Engineering | Geometry, algebraic | Systems theory | Vibration | Engineering | Control Engineering | Vibration, Dynamical Systems, Control | Systems Theory, Control | Algebraic GeometryAdditional physical formats: Printed edition:: No titleOnline resources: Click here to access online
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.
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.