Constructions of Strict Lyapunov Functions
Michael Malisoff · Frédéric Mazenc
Jun 2009 · Springer Science & Business Media
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About this eBook
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.
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A Google user
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15 August 2009
This book is an absolute masterpiece. The constructions are very useful and the authors really have a knack for explaining complex ideas in a clear and concise way. I definitely recommend this book to anyone working in control engineering.
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