Converse Lyapunov function theory guarantees the existence of strict Lyapunovfunctions 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 solvedthrough 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 theeffects of uncertainty. Readers will benefit from the authors’ mathematical rigor and unifying, design-oriented approach, as well as the numerous worked examples. Provides the reader with a user-friendly framework for building Lyapunov functions in novel settings Helps the reader with feedback design and in quantifying the effects of system uncertainty INDICE: Part I: Background.- Background on Nonlinear Systems.- Review of Lyapunov Functions.- Part II: Time Invariant Case.- Matrosov Conditions: SimpleCase.- Jurdjevic–Quinn Conditions.- Systems Satisfying the Conditions of LaSalle.- Part III: Time Varying Case.- Strictification: Basic Results.- Backstepping for Time Varying Systems.- Matrosov Conditions: General Case.- Adaptively Controlled Sytems.- Part IV: Systems with Multiple Time Scales.- Rapidly Time Varying Systems.- Slowly Time Varying Systems.- Hybrid Time Varying Systems.- Appendices: Some Lemmas; Converse Theory.
- ISBN: 978-1-84882-534-5
- Editorial: Springer
- Encuadernacion: Cartoné
- Páginas: 400
- Fecha Publicación: 01/08/2009
- Nº Volúmenes: 1
- Idioma: Inglés