Constructions of Strict Lyapunov Functions

Michael Malisoff, Frédéric Mazenc (Autoren)

Buch | Softcover

386 Seiten

2014
Springer London Ltd (Verlag)
978-1-4471-5782-3 (ISBN)

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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.

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.

Erscheint lt. Verlag	30.10.2014
Reihe/Serie	Communications and Control Engineering
Zusatzinfo	XVI, 386 p.
Verlagsort	England
Sprache	englisch
Maße	155 x 235 mm
Themenwelt	Informatik ► Theorie / Studium ► Künstliche Intelligenz / Robotik
	Informatik ► Weitere Themen ► CAD-Programme
	Mathematik / Informatik ► Mathematik ► Algebra
	Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
	Technik ► Elektrotechnik / Energietechnik
	Technik ► Maschinenbau
ISBN-10	1-4471-5782-6 / 1447157826
ISBN-13	978-1-4471-5782-3 / 9781447157823
Zustand	Neuware