
Homogeneous Polynomial Forms for Robustness Analysis of Uncertain Systems
Springer (Publisher)
Published on 21. July 2009
Book
Paperback/Softback
XVIII, 198 pages
978-1-84882-780-6 (ISBN)
Description
It is well known that a large number of problems relevant to the control ?eld can be formulatedas optimizationproblems. For long time, the classical approachhas been to look for a closed form solution to the speci?c optimizationproblems at hand. The last decade has seen a noticeable shift in the meaning of "closed form" solution. The formidable increase of computationalpower has dramatically changed the fe- ing of theoreticians as well as of practitioners about what is meant by tractable and untractableproblems. A main issue regardsconvexity. From a theoretical viewpoint, there has been a large amount of work in the directions of "convexifying" nonc- vex problems and studying structural features of convex problems. On the other hand, extremely powerful algorithmsfor the solution of convexproblemshave been devised in the last two decades. Clearly, the fact that a wide variety of engine- ing problems can be formulated as convex problems has strongly motivated efforts in this direction. The control ?eld is not an exception in this sense: many pr- lems in robust control, identi?cation and nonlinear control have been recognized as convex problems.
Moreover, convex relaxations of nonconvex problems have been intensively investigated, as they provide an effective tool for bounding the optimal solution of the original problem. As far as robust control is concerned, it is known since long time that several classes of problemscan be reducedto testing positivity of suitable polynomials.
Moreover, convex relaxations of nonconvex problems have been intensively investigated, as they provide an effective tool for bounding the optimal solution of the original problem. As far as robust control is concerned, it is known since long time that several classes of problemscan be reducedto testing positivity of suitable polynomials.
Reviews / Votes
From the reviews:
"The book describes convex optimization techniques to deal with stability and performance evaluation for linear dynamical systems subject to parametric uncertainty. . In summary, the book is a welcome and timely addition to the technical literature, written by leading experts in the field. It is aimed at systems and control researchers willing to explore further than mainstream LMI Lyapunov analysis techniques, with the possibility of trading off between conservatism and computational burden." (Didier Henrion, Mathematical Reviews, Issue 2010 g)More details
Series
Edition
2009 ed.
Language
English
Place of publication
London
United Kingdom
Target group
Professional and scholarly
Research
Product notice
Paperback (trade)
Unsewn / adhesive bound
Illustrations
17 s/w Abbildungen
XVIII, 198 p. 17 illus.
Dimensions
Height: 241 mm
Width: 167 mm
Thickness: 23 mm
Weight
480 gr
ISBN-13
978-1-84882-780-6 (9781848827806)
DOI
10.1007/978-1-84882-781-3
Schweitzer Classification
Other editions
Additional editions

Graziano Chesi | Andrea Garulli | Alberto Tesi
Homogeneous Polynomial Forms for Robustness Analysis of Uncertain Systems
E-Book
07/2009
Springer
€96.29
Available for download
Content
Positive Forms.- Positivity Gap.- Robustness with Time-varying Uncertainty.- Robustness with Time-invariant Uncertainty.- Robustness with Bounded-rate Time-varying Uncertainty.- Distance Problems with Applications to Robust Control.