Well-posed linear systems - a survey with emphasis on conservative systems

George Weiss; Olof Staffans; Marius Tucsnak

International Journal of Applied Mathematics and Computer Science (2001)

  • Volume: 11, Issue: 1, page 7-33
  • ISSN: 1641-876X

Abstract

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We survey the literature on well-posed linear systems, which has been an area of rapid development in recent years. We examine the particular subclass of conservative systems and its connections to scattering theory. We study some transformations of well-posed systems, namely duality and time-flow inversion, and their effect on the transfer function and the generating operators. We describe a simple way to generate conservative systems via a second-order differential equation in a Hilbert space. We give results about the stability, controllability and observability of such conservative systems and illustrate these with a system modeling a controlled beam.

How to cite

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Weiss, George, Staffans, Olof, and Tucsnak, Marius. "Well-posed linear systems - a survey with emphasis on conservative systems." International Journal of Applied Mathematics and Computer Science 11.1 (2001): 7-33. <http://eudml.org/doc/207507>.

@article{Weiss2001,
abstract = {We survey the literature on well-posed linear systems, which has been an area of rapid development in recent years. We examine the particular subclass of conservative systems and its connections to scattering theory. We study some transformations of well-posed systems, namely duality and time-flow inversion, and their effect on the transfer function and the generating operators. We describe a simple way to generate conservative systems via a second-order differential equation in a Hilbert space. We give results about the stability, controllability and observability of such conservative systems and illustrate these with a system modeling a controlled beam.},
author = {Weiss, George, Staffans, Olof, Tucsnak, Marius},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {beam equation; conservative system; well-posed linear system; regular linear system; differential equations in Hilbert space; operator semigroup; scattering theory; time-flow-inversion; time-flow inversion; second-order damped differential equations in Hilbert space; passive systems; stability; controllability; observability},
language = {eng},
number = {1},
pages = {7-33},
title = {Well-posed linear systems - a survey with emphasis on conservative systems},
url = {http://eudml.org/doc/207507},
volume = {11},
year = {2001},
}

TY - JOUR
AU - Weiss, George
AU - Staffans, Olof
AU - Tucsnak, Marius
TI - Well-posed linear systems - a survey with emphasis on conservative systems
JO - International Journal of Applied Mathematics and Computer Science
PY - 2001
VL - 11
IS - 1
SP - 7
EP - 33
AB - We survey the literature on well-posed linear systems, which has been an area of rapid development in recent years. We examine the particular subclass of conservative systems and its connections to scattering theory. We study some transformations of well-posed systems, namely duality and time-flow inversion, and their effect on the transfer function and the generating operators. We describe a simple way to generate conservative systems via a second-order differential equation in a Hilbert space. We give results about the stability, controllability and observability of such conservative systems and illustrate these with a system modeling a controlled beam.
LA - eng
KW - beam equation; conservative system; well-posed linear system; regular linear system; differential equations in Hilbert space; operator semigroup; scattering theory; time-flow-inversion; time-flow inversion; second-order damped differential equations in Hilbert space; passive systems; stability; controllability; observability
UR - http://eudml.org/doc/207507
ER -

References

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Citations in EuDML Documents

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  1. George Weiss, Marius Tucsnak, How to get a conservative well-posed linear system out of thin air. Part I. Well-posedness and energy balance
  2. George Weiss, Marius Tucsnak, How to get a conservative well-posed linear system out of thin air. Part I. Well-posedness and energy balance
  3. Olof Staffans, J-energy preserving well-posed linear systems
  4. Bao-Zhu Guo, Zhi-Xiong Zhang, On the well-posedness and regularity of the wave equation with variable coefficients
  5. Denis Matignon, Christophe Prieur, Asymptotic stability of linear conservative systems when coupled with diffusive systems
  6. Denis Matignon, Christophe Prieur, Asymptotic stability of linear conservative systems when coupled with diffusive systems

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