- Provides the reader with a unique study of input-to-state stability for partial differential equations
- Offers the first systematic study of PDEs with non-local terms
- Equips the reader for a large number of applications that are at the core of many scientific disciplines
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- About this book
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This book lays the foundation for the study of input-to-state stability (ISS) of partial differential equations (PDEs) predominantly of two classes—parabolic and hyperbolic. This foundation consists of new PDE-specific tools.
In addition to developing ISS theorems, equipped with gain estimates with respect to external disturbances, the authors develop small-gain stability theorems for systems involving PDEs. A variety of system combinations are considered:
- PDEs (of either class) with static maps;
- PDEs (again, of either class) with ODEs;
- PDEs of the same class (parabolic with parabolic and hyperbolic with hyperbolic); and
- feedback loops of PDEs of different classes (parabolic with hyperbolic).
- PDEs (of either class) with static maps;
- About the authors
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Iasson Karafyllis is an Associate Professor in the Department of Mathematics, NTUA, Greece. He is a coauthor (with Z.-P. Jiang) of the book Stability and Stabilization of Nonlinear Systems, Springer-Verlag London (Series: Communications and Control Engineering), 2011 and a coauthor (with M. Krstic) of the book Predictor Feedback for Delay Systems: Implementations and Approximations, Birkhäuser, Boston (Series: Mathematics, Systems & Control: Foundations & Applications), 2017. Since 2013 he is an Associate Editor for the International Journal of Control and for the IMA Journal of Mathematical Control and Information. His research interests include mathematical control theory and nonlinear systems theory.
Miroslav Krstic is Distinguished Professor, Alspach endowed chair, founding director of the Cymer Center for Control Systems and Dynamics, and Senior Associate Vice Chancellor for Research at UC San Diego. Krstic is Fellow of IEEE, IFAC, ASME, SIAM, AAAS, and IET (UK), Associate Fellow of AIAA, and foreign member of the Academy of Engineering of Serbia. He has received ASME Oldenburger Medal, ASME Nyquist Lecture Prize, ASME Paynter Outstanding Investigator Award, the PECASE, NSF Career, and ONR Young Investigator awards, the Axelby and Schuck paper prizes, the Chestnut textbook prize, and the first UCSD Research Award given to an engineer. Krstic has also been awarded the Distinguished Visiting Fellowship of the Royal Academy of Engineering and Invitation Fellowship of the Japan Society for the Promotion of Science. Krstic has coauthored twelve books on adaptive, nonlinear, and stochastic control, extremum seeking, control of PDE systems including turbulent flows, and control of delay systems. - Reviews
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“This is a beautiful book, highly recommended to researchers and, as a textbook, to post-graduates. The graphical conditions are excellent.” (Vladimir Răsvan, zbMath 1416.93004, 2019)
- Table of contents (11 chapters)
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Preview
Pages 1-16
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Existence/Uniqueness Results for Hyperbolic PDEs
Pages 19-38
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ISS in Spatial L p Norms for Hyperbolic PDEs
Pages 39-56
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Existence/Uniqueness Results for Parabolic PDEs
Pages 61-92
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ISS in Spatial L2 and H1 Norms
Pages 93-140
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Table of contents (11 chapters)
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Bibliographic Information
- Bibliographic Information
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- Book Title
- Input-to-State Stability for PDEs
- Authors
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- Iasson Karafyllis
- Miroslav Krstic
- Series Title
- Communications and Control Engineering
- Copyright
- 2019
- Publisher
- Springer International Publishing
- Copyright Holder
- Springer Nature Switzerland AG
- eBook ISBN
- 978-3-319-91011-6
- DOI
- 10.1007/978-3-319-91011-6
- Hardcover ISBN
- 978-3-319-91010-9
- Softcover ISBN
- 978-3-030-08155-3
- Series ISSN
- 0178-5354
- Edition Number
- 1
- Number of Pages
- XVI, 287
- Number of Illustrations
- 1 illustrations in colour
- Topics
