Constructions of Strict Lyapunov Functions

2009
ISBN: 978-1-4471-5782-3
Verlag: Springer

Buch, Englisch, 386 Seiten, Previously published in hardcover, Format (B × H): 155 mm x 235 mm, Gewicht: 610 g

Reihe: Communications and Control Engineering

Converse Lyapunov function theory guarantees the existence of strict Lyapunov functions in many situations, but the functions it provides are often abstract and nonexplicit, and therefore may not lend themselves to engineering applications. Often, even when a system is known to be stable, one still needs explicit Lyapunov functions; however, once an appropriate strict Lyapunov function has been constructed, many robustness and stabilization problems can be solved through standard feedback designs or robustness arguments. Non-strict Lyapunov functions are often readily constructed.

This book contains a broad repertoire of Lyapunov constructions for nonlinear systems, focusing on methods for transforming non-strict Lyapunov functions into strict ones. Their explicitness and simplicity make them suitable for feedback design, and for quantifying the effects of uncertainty. Readers will benefit from the authors’ mathematical rigor and unifying, design-oriented approach, as well as the numerous worked examples.

Zielgruppe

Research

Autoren/Hrsg.

Mazenc, Frédéric

Malisoff, Michael

Fachgebiete

• Technische Wissenschaften Maschinenbau | Werkstoffkunde Technische Mechanik | Werkstoffkunde Statik, Dynamik, Kinetik, Kinematik
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
• Technische Wissenschaften Technik Allgemein Modellierung & Simulation
• Mathematik | Informatik Mathematik Mathematische Analysis Variationsrechnung
• Technische Wissenschaften Elektronik | Nachrichtentechnik Elektronik Überwachungstechnik
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Computeranwendungen in der Mathematik

Inhaltsverzeichnis

Background.- Background on Nonlinear Systems.- Review of Lyapunov Functions.- Time-Invariant Case.- Matrosov Conditions: Simple Case.- Jurdjevic-Quinn Conditions.- Systems Satisfying the Conditions of LaSalle.- Time-Varying Case.- Strictification: Basic Results.- Backstepping for Time-Varying Systems.- Matrosov Conditions: General Case.- Adaptively Controlled Systems.- Systems with Multiple Time Scales.- Rapidly Time-Varying Systems.- Slowly Time-Varying Systems.- Hybrid Time-Varying Systems.