Graziano Chesi, Andrea Garulli, Alberto Tesi, Antonio Vicino

Homogeneous Polynomial Forms for Robustness Analysis of Uncertain Systems (eBook, PDF)

• Format: PDF

Produktbeschreibung

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.

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Produktdetails

• Verlag: Springer-Verlag GmbH
• Seitenzahl: 198
• Erscheinungstermin: 13. Juli 2009
• Englisch
• ISBN-13: 9781848827813
• Artikelnr.: 43886377

Inhaltsangabe

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.

Rezensionen

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)