Ebook: Fourier Series in Control Theory
- Tags: Systems Theory Control, Calculus of Variations and Optimal Control, Optimization
- Series: Springer Monographs in Mathematics
- Year: 2005
- Publisher: Springer-Verlag New York
- Edition: 1
- Language: English
- pdf
Advance Praise for Fourier Series in Control Theory:
It has been known since 1967 that a wide variety of sets of complex exponential functions play an important role in the control theory of systems governed by partial differential equations. Up until now, the relevant literature has been scattered among various journal articles, a survey paper by myself in SIAM Review in 1978, and the book, Families of Exponentials, by S. Avdonin and S. Ivanov (1995). Fourier Series in Control Theory successfully gathers all of the available theory of these "nonharmonic Fourier series" in one place, combining published results with new results, to create a unique source of such material for practicing applied mathematicians, engineers, and other scientific professionals.
- David Russell, Virginia Polytechnic Institute and State University
This monograph will be of interest to experts and researchers, as well as graduate students in such courses as control series and harmonic analysis. Starting with an overview of the problems of observability, controllability, and stabilization of linear systems and their interconnections, the text contains complete proofs along with a short, simplified, presentation of some properties of Bessel functions for the convenience of the reader. Only basic knowledge of functional analysis is required.
Advance Praise for Fourier Series in Control Theory:
It has been known since 1967 that a wide variety of sets of complex exponential functions play an important role in the control theory of systems governed by partial differential equations. Up until now, the relevant literature has been scattered among various journal articles, a survey paper by myself in SIAM Review in 1978, and the book, Families of Exponentials, by S. Avdonin and S. Ivanov (1995). Fourier Series in Control Theory successfully gathers all of the available theory of these "nonharmonic Fourier series" in one place, combining published results with new results, to create a unique source of such material for practicing applied mathematicians, engineers, and other scientific professionals.
- David Russell, Virginia Polytechnic Institute and State University
This monograph will be of interest to experts and researchers, as well as graduate students in such courses as control series and harmonic analysis. Starting with an overview of the problems of observability, controllability, and stabilization of linear systems and their interconnections, the text contains complete proofs along with a short, simplified, presentation of some properties of Bessel functions for the convenience of the reader. Only basic knowledge of functional analysis is required.
Advance Praise for Fourier Series in Control Theory:
It has been known since 1967 that a wide variety of sets of complex exponential functions play an important role in the control theory of systems governed by partial differential equations. Up until now, the relevant literature has been scattered among various journal articles, a survey paper by myself in SIAM Review in 1978, and the book, Families of Exponentials, by S. Avdonin and S. Ivanov (1995). Fourier Series in Control Theory successfully gathers all of the available theory of these "nonharmonic Fourier series" in one place, combining published results with new results, to create a unique source of such material for practicing applied mathematicians, engineers, and other scientific professionals.
- David Russell, Virginia Polytechnic Institute and State University
This monograph will be of interest to experts and researchers, as well as graduate students in such courses as control series and harmonic analysis. Starting with an overview of the problems of observability, controllability, and stabilization of linear systems and their interconnections, the text contains complete proofs along with a short, simplified, presentation of some properties of Bessel functions for the convenience of the reader. Only basic knowledge of functional analysis is required.
Content:
Front Matter....Pages I-IX
Introduction....Pages 1-7
Observation, Control, and Stabilization....Pages 9-31
Well-Posedness in a Riesz Basis Setting....Pages 33-56
Observability of Strings....Pages 57-82
Observability of Beams....Pages 83-88
Vector Sum Estimates....Pages 89-126
Problems on Spherical Domains....Pages 127-152
Multidimensional Ingham-Type Theorems....Pages 153-172
A General Ingham-Type Theorem....Pages 173-198
Problems with Weakened Gap Conditions....Pages 199-215
Back Matter....Pages 217-226
Advance Praise for Fourier Series in Control Theory:
It has been known since 1967 that a wide variety of sets of complex exponential functions play an important role in the control theory of systems governed by partial differential equations. Up until now, the relevant literature has been scattered among various journal articles, a survey paper by myself in SIAM Review in 1978, and the book, Families of Exponentials, by S. Avdonin and S. Ivanov (1995). Fourier Series in Control Theory successfully gathers all of the available theory of these "nonharmonic Fourier series" in one place, combining published results with new results, to create a unique source of such material for practicing applied mathematicians, engineers, and other scientific professionals.
- David Russell, Virginia Polytechnic Institute and State University
This monograph will be of interest to experts and researchers, as well as graduate students in such courses as control series and harmonic analysis. Starting with an overview of the problems of observability, controllability, and stabilization of linear systems and their interconnections, the text contains complete proofs along with a short, simplified, presentation of some properties of Bessel functions for the convenience of the reader. Only basic knowledge of functional analysis is required.
Content:
Front Matter....Pages I-IX
Introduction....Pages 1-7
Observation, Control, and Stabilization....Pages 9-31
Well-Posedness in a Riesz Basis Setting....Pages 33-56
Observability of Strings....Pages 57-82
Observability of Beams....Pages 83-88
Vector Sum Estimates....Pages 89-126
Problems on Spherical Domains....Pages 127-152
Multidimensional Ingham-Type Theorems....Pages 153-172
A General Ingham-Type Theorem....Pages 173-198
Problems with Weakened Gap Conditions....Pages 199-215
Back Matter....Pages 217-226
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