Nonsmooth Lyapunov Analysis in Finite and Infinite Dimensions provides helpful tools for the treatment of a broad class of dynamical systems that are governed, not only by ordinary differential equations but also by partial and functional differential equations. Existing Lyapunov constructions are extended to discontinuous systemsthose with variable structure and impactby the involvement of nonsmooth Lyapunov functions. The general theoretical presentation is illustrated by control-related applications; the nonsmooth Lyapunov construction is particularly applied to the tuning of sliding-mode controllers in the presence of mismatched disturbances and to orbital stabilization of the bipedal gate. The nonsmooth construction is readily extendible to the control and identification of distributed-parameter and time-delay systems.
The first part of the book outlines the relevant fundamentals of benchmark models and mathematical basics. The second concentrates on theconstruction of nonsmooth Lyapunov functions. Part III covers design and applications material.
This book will benefit the academic research and graduate student interested in the mathematics of Lyapunov equations and variable-structure control, stability analysis and robust feedback design for discontinuous systems. It will also serve the practitioner working with applications of such systems. The reader should have some knowledge of dynamical systems theory, but no background in discontinuous systems is requiredthey are thoroughly introduced in both finite- and infinite-dimensional settings.

Focuses on the methodology of the construction of nonsmooth Lyapunov functions, given in both finite- and infinite-dimensional settings Presents theoretical development, relying on up-to-date nonsmooth Lyapunov functions and supported by modern engineering applications Provides explicit applicability to feedback design and tuning of sliding mode controllers under unmatched external disturbances

Autorentext

Yury Orlov received his M.S. degree from the Mechanical-Mathematical Faculty of Moscow State University, in 1979, the Ph.D. degree in Physics and Mathematics from the Institute of Control Science, Moscow, in 1984, and the Dr.Sc. degree also in Physics and Mathematics from Moscow Aviation Institute, in 1990. He started his scientific career in the Institute of Control Science in 1979 and since 1993, he has been a Full Professor of the Electronics and Telecommunication Department, Scientific Research and Advanced Studies Center of Ensenada, Mexico. During the scientific career he shared visiting/temporal professor positions in Moscow Aviation Institute, CESAME (Catholic University in Louvain, Belgium), Ecole Central de Lille (France), Robotics Laboratory of Versalle University (France), INRIA (Grenoble, France), IRCCYN (University of Nantes, France), University of Angers (France), University of Cagliari (Italy), University of Kent (UK), and Lund University (Sweden). The research interests include  mathematical methods in control, analysis and synthesis of nonlinear, nonsmooth, discontinuous, time delay, distributed parameter systems, and applications to electromechanical systems. He has authored and co-authored about 250 journal and conference papers in the above areas as well as four monographs, including the recent ones called Discontinuous Systems-Lyapunov Analysis and Robust Synthesis under Uncertainty Conditions (Springer Communications & Control Engineering series, 2009) and Advanced H-infinity Control - Towards Nonsmooth Theory Applications (Birkhauser, Systems & Control: Foundations & Applications series, 2014).

Klappentext

Nonsmooth Lyapunov Analysis in Finite and Infinite Dimensions provides helpful tools for the treatment of a broad class of dynamical systems that are governed, not only by ordinary differential equations but also by partial and functional differential equations. Existing Lyapunov constructions are extended to discontinuous systems those with variable structure and impact by the involvement of nonsmooth Lyapunov functions. The general theoretical presentation is illustrated by control-related applications; the nonsmooth Lyapunov construction is particularly applied to the tuning of sliding-mode controllers in the presence of mismatched disturbances and to orbital stabilization of the bipedal gate. The nonsmooth construction is readily extendible to the control and identification of distributed-parameter and time-delay systems. The first part of the book outlines the relevant fundamentals of benchmark models and mathematical basics. The second concentrates on theconstruction of nonsmooth Lyapunov functions. Part III covers design and applications material. This book will benefit the academic research and graduate student interested in the mathematics of Lyapunov equations and variable-structure control, stability analysis and robust feedback design for discontinuous systems. It will also serve the practitioner working with applications of such systems. The reader should have some knowledge of dynamical systems theory, but no background in discontinuous systems is required they are thoroughly introduced in both finite- and infinite-dimensional settings.

Inhalt

Part I: Introduction.- Chapter 1. Benchmark Models.- Chapter 2. Mathematical Background.- Chapter 3. Mathematical Tools of Dynamic Systems in Hilbert Spaces.- Part II: Construction of Nonsmooth Lyapunov Functions.- Chapter 4. Modern Lyapunov Tools.- Chapter 5. Control Lyapunov Functions.- Part III: Lyapunov Redesign.- Chapter 6. Lyapunov-based Tuning.- Chapter 7. Lyapunov Approach to Adaptive Identication and Control in Innite-dimensional Setting.- Chapter 8. Control Applications.