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Nonsmooth Lyapunov analysis in finit...

Orlov, Yury.

Nonsmooth Lyapunov analysis in finite and infinite dimensions

Record Type:	Electronic resources : Monograph/item
Title/Author:	Nonsmooth Lyapunov analysis in finite and infinite dimensionsby Yury Orlov.
Author:	Orlov, Yury.
Published:	Cham :Springer International Publishing :2020.
Description:	xix, 340 p. :ill., digital ;24 cm.
Contained By:	Springer eBooks
Subject:	Lyapunov functions.
Online resource:	https://doi.org/10.1007/978-3-030-37625-3
ISBN:	9783030376253$q(electronic bk.)

Nonsmooth Lyapunov analysis in finite and infinite dimensions
Orlov, Yury.

Nonsmooth Lyapunov analysis in finite and infinite dimensions[electronic resource] /by Yury Orlov. - Cham :Springer International Publishing :2020. - xix, 340 p. :ill., digital ;24 cm. - Communications and control engineering,0178-5354. - Communications and control engineering..

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 Identiﬁcation and Control in Inﬁnite-dimensional Setting -- Chapter 8. Control Applications.

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 the construction 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.

ISBN: 9783030376253$q(electronic bk.)

Standard No.: 10.1007/978-3-030-37625-3doiSubjects--Topical Terms:

306549
Lyapunov functions.

LC Class. No.: QA871 / .O756 2020

Dewey Class. No.: 515.392

Nonsmooth Lyapunov analysis in finite and infinite dimensions
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505 0 $a 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 Identiﬁcation and Control in Inﬁnite-dimensional Setting -- Chapter 8. Control Applications.
520 $a 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 the construction 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.
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