Homogeneous Polynomial Forms for Robustness Analysis of Uncertain Systems
Published on 13. July 2009
XVIII, 198 pages
978-1-84882-781-3 (ISBN)
Description
This book presents a number of techniques for robustness analysis of uncertain systems. The theoretical basis for their development is derived from the application of convex optimization tools to problems involving positivity of homogeneous polynomial forms. Usually, stability and performance analysis of dynamic systems affected by structured uncertainties, requires the solution of non-convex optimization problems. Constructing a family of convex relaxations, namely convex optimisations, can provide upper or lower bound to the original problem. In this book convex relaxations for several robustness problems are derived by exploiting and providing new results on the theory of homogeneous polynomial forms. A framework is introduced for dealing with positivity of homogeneous forms via the solution of linear matrix inequalities, with examples including Lyapunov analysis of uncertain systems, computation of the parametric robust stability margin, and robust performance analysis for polytopic systems.
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
Other editions
Additional editions
Graziano Chesi | Andrea Garulli | Alberto Tesi
Homogeneous Polynomial Forms for Robustness Analysis of Uncertain Systems
Book
07/2009
Springer
€106.99
Shipment within 15-20 days
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.
