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<p>The second edition of&#xa0;<em>Generalized Homogeneity in Systems and Control</em>&#xa0;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.</p><p>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.</p><p><em>Generalized Homogeneity in Systems and Control Volume II</em>&#xa0;(second edition) moves from stability analysis to the design of controllers for various systems. Key features of the book include:</p><ul> <li>mathematical models of dynamical systems in infinite-dimensional spaces;</li> <li>the theory of linear dilations in Banach and Hilbert spaces (including Lebesgue and Sobolev spaces);</li> <li>abstract differential equations with homogeneous operators (including differential operators);</li> <li>rewritten, reorganized chapters with the addition of substantial new material;</li> <li>robustness analysis of infinite-dimensional homogeneous systems;</li> <li>homogeneous control in a Hilbert space; and</li> <li>consistent discretization of homogeneous systems.</li></ul><p>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.</p>

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Generalized Homogeneity in Systems and Control Volume II

  • 书籍

  • 发表日期：

    2025年

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  • Andrey Polyakov

摘要

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.