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Control of wave and beam PDEsthe Rie...

Guo, Bao-Zhu.

Control of wave and beam PDEsthe Riesz basis approach /

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Control of wave and beam PDEsby Bao-Zhu Guo, Jun-Min Wang.
其他題名:	the Riesz basis approach /
作者:	Guo, Bao-Zhu.
其他作者:	Wang, Jun-Min.
出版者:	Cham :Springer International Publishing :2019.
面頁冊數:	xi, 596 p. :ill., digital ;24 cm.
Contained By:	Springer eBooks
標題:	Riesz spaces.
電子資源:	https://doi.org/10.1007/978-3-030-12481-6
ISBN:	9783030124816$q(electronic bk.)

Control of wave and beam PDEsthe Riesz basis approach /
Guo, Bao-Zhu.

Control of wave and beam PDEsthe Riesz basis approach /[electronic resource] :by Bao-Zhu Guo, Jun-Min Wang. - Cham :Springer International Publishing :2019. - xi, 596 p. :ill., digital ;24 cm. - Communications and control engineering,0178-5354. - Communications and control engineering..

Chapter 1. Preliminaries -- Chapter 2. Bases in Hilbert spaces -- Chapter 3. Riesz basis generation: comparison method -- Chapter 4. Riesz basis generation: dual basis approach -- Chapter 5. Riesz basis generation: Green function approach -- Chapter 6. Stabilization of coupled systems.

Control of Wave and Beam PDEs is a concise, self-contained introduction to Riesz bases in Hilbert space and their applications to control systems described by partial differential equations (PDEs) The authors discuss classes of systems that satisfy the spectral determined growth condition, the problem of stability, and the relationship between fulfillment of the condition and stability. Using the (fundamental) Riesz-basis property, the book shows how controllability, observability, stability, etc., can be derived for a linear system. The text provides a crash course in the mathematical theory of Riesz bases so that a reader can quickly understand this powerful method of dealing with linear PDEs. It introduces several important methods for achieving the Riesz basis property through spectral analysis, as well as new approaches including treatment of systems coupled through boundary weak connections. The book moves from a discussion of mathematical preliminaries through bases in Hilbert Spaces to applications to Euler-Bernoulli and Rayleigh beam equations and hybrid systems. The final chapter expands the use of the book's methods to applications in other systems. Many typical examples, representing physical systems, are discussed in the text. The book is suitable not only for applied mathematicians seeking a powerful tool to understand control systems, but also for control engineers interested in the mathematics of PDE systems.

ISBN: 9783030124816$q(electronic bk.)

Standard No.: 10.1007/978-3-030-12481-6doiSubjects--Topical Terms:

665361
Riesz spaces.

LC Class. No.: QA322 / .G863 2019

Dewey Class. No.: 515.73

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505 0 $a Chapter 1. Preliminaries -- Chapter 2. Bases in Hilbert spaces -- Chapter 3. Riesz basis generation: comparison method -- Chapter 4. Riesz basis generation: dual basis approach -- Chapter 5. Riesz basis generation: Green function approach -- Chapter 6. Stabilization of coupled systems.
520 $a Control of Wave and Beam PDEs is a concise, self-contained introduction to Riesz bases in Hilbert space and their applications to control systems described by partial differential equations (PDEs) The authors discuss classes of systems that satisfy the spectral determined growth condition, the problem of stability, and the relationship between fulfillment of the condition and stability. Using the (fundamental) Riesz-basis property, the book shows how controllability, observability, stability, etc., can be derived for a linear system. The text provides a crash course in the mathematical theory of Riesz bases so that a reader can quickly understand this powerful method of dealing with linear PDEs. It introduces several important methods for achieving the Riesz basis property through spectral analysis, as well as new approaches including treatment of systems coupled through boundary weak connections. The book moves from a discussion of mathematical preliminaries through bases in Hilbert Spaces to applications to Euler-Bernoulli and Rayleigh beam equations and hybrid systems. The final chapter expands the use of the book's methods to applications in other systems. Many typical examples, representing physical systems, are discussed in the text. The book is suitable not only for applied mathematicians seeking a powerful tool to understand control systems, but also for control engineers interested in the mathematics of PDE systems.
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