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Polyakov, Andrey.

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Generalized homogeneity in systems and control.. Volume II,. Infinite-dimensional systems

Record Type:	Electronic resources : Monograph/item
Title/Author:	Generalized homogeneity in systems and control./ by Andrey Polyakov.
remainder title:	Infinite-dimensional systems
Author:	Polyakov, Andrey.
Published:	Cham :Springer Nature Switzerland : : 2025.,
Description:	xvi, 379 p. :ill. (some col.), digital ;24 cm.
[NT 15003449]:	Chapter 1. Introduction to Abstract Homogeneity -- Chapter 2. Abstract Differential Equations -- Chapter 3. Lyapunov Methods for Abstract Differential Equations -- Chapter 4. Linear Dilations in Abstract Spaces -- Chapter 5. Infinite-Dimensional Homogeneous Mappings -- Chapter 6. Analysis of Infinite-Dimensional Homogeneous Systems -- Chapter 7. Discretization of Infinite-Dimensional Homogeneous Systems -- Chapter 8. Homogeneous Stabilization of Infinite-Dimensional Systems.
Contained By:	Springer Nature eBook
Subject:	Control theory. -
Online resource:	https://doi.org/10.1007/978-3-031-77496-6
ISBN:	9783031774966

Generalized homogeneity in systems and control.. Volume II,. Infinite-dimensional systems
Polyakov, Andrey.

Generalized homogeneity in systems and control.Volume II,Infinite-dimensional systems[electronic resource] /Infinite-dimensional systemsby Andrey Polyakov. - Second edition. - Cham :Springer Nature Switzerland :2025. - xvi, 379 p. :ill. (some col.), digital ;24 cm. - Communications and control engineering,2197-7119. - Communications and control engineering..

Chapter 1. Introduction to Abstract Homogeneity -- Chapter 2. Abstract Differential Equations -- Chapter 3. Lyapunov Methods for Abstract Differential Equations -- Chapter 4. Linear Dilations in Abstract Spaces -- Chapter 5. Infinite-Dimensional Homogeneous Mappings -- Chapter 6. Analysis of Infinite-Dimensional Homogeneous Systems -- Chapter 7. Discretization of Infinite-Dimensional Homogeneous Systems -- Chapter 8. Homogeneous Stabilization of Infinite-Dimensional Systems.

The second edition of Generalized Homogeneity in Systems and Control is an introduction to the theory of homogeneous systems, useful for the simplification of many types of nonlinear control problem. It propounds methods that can be employed when linearization proves unsuitable and provides a unified approach to stability and robustness analysis, control and observer design, and system discretization. The second edition splits the coverage of homogeneity, allowing expanded coverage of finite-dimensional systems (in Volume I) and infinite-dimensional systems (in this book). The results are better systematized and easier for readers to study and assimilate. Generalized Homogeneity in Systems and Control Volume II (second edition) moves from stability analysis to the design of controllers for various systems. Key features of the book include: mathematical models of dynamical systems in infinite-dimensional spaces; the theory of linear dilations in Banach and Hilbert spaces (including Lebesgue and Sobolev spaces); abstract differential equations with homogeneous operators (including differential operators); rewritten, reorganized chapters with the addition of substantial new material; robustness analysis of infinite-dimensional homogeneous systems; homogeneous control in a Hilbert space; and consistent discretization of homogeneous systems. Illustrative examples - numerical results, computer simulations and real experiments - support all the theoretical material. The coverage of infinite-dimensional systems presented in this book will be of interest to graduate students of control theory and applied mathematics and academic researchers in control.

ISBN: 9783031774966

Standard No.: 10.1007/978-3-031-77496-6doiSubjects--Topical Terms:

535880
Control theory.

LC Class. No.: QA402.3

Dewey Class. No.: 629.8312

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490 1 $a Communications and control engineering, $x 2197-7119
505 0 $a Chapter 1. Introduction to Abstract Homogeneity -- Chapter 2. Abstract Differential Equations -- Chapter 3. Lyapunov Methods for Abstract Differential Equations -- Chapter 4. Linear Dilations in Abstract Spaces -- Chapter 5. Infinite-Dimensional Homogeneous Mappings -- Chapter 6. Analysis of Infinite-Dimensional Homogeneous Systems -- Chapter 7. Discretization of Infinite-Dimensional Homogeneous Systems -- Chapter 8. Homogeneous Stabilization of Infinite-Dimensional Systems.
520 $a The second edition of Generalized Homogeneity in Systems and Control is an introduction to the theory of homogeneous systems, useful for the simplification of many types of nonlinear control problem. It propounds methods that can be employed when linearization proves unsuitable and provides a unified approach to stability and robustness analysis, control and observer design, and system discretization. The second edition splits the coverage of homogeneity, allowing expanded coverage of finite-dimensional systems (in Volume I) and infinite-dimensional systems (in this book). The results are better systematized and easier for readers to study and assimilate. Generalized Homogeneity in Systems and Control Volume II (second edition) moves from stability analysis to the design of controllers for various systems. Key features of the book include: mathematical models of dynamical systems in infinite-dimensional spaces; the theory of linear dilations in Banach and Hilbert spaces (including Lebesgue and Sobolev spaces); abstract differential equations with homogeneous operators (including differential operators); rewritten, reorganized chapters with the addition of substantial new material; robustness analysis of infinite-dimensional homogeneous systems; homogeneous control in a Hilbert space; and consistent discretization of homogeneous systems. Illustrative examples - numerical results, computer simulations and real experiments - support all the theoretical material. The coverage of infinite-dimensional systems presented in this book will be of interest to graduate students of control theory and applied mathematics and academic researchers in control.
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