Overview
- Provides a detailed study of the concept of rotation and of the solutions
- of linear nonautonomous Hamiltonian systems of general dimension
- Explores the applications of linear Hamiltonian systems to
- questions arising in classical oscillation theory of such systems, and to the
- theory of linear control systems with time-varying coefficients
- Applies known results of the theory of periodic Hamiltonian systems to the general nonautonomous case and presents various new properties
Part of the book series: Developments in Mathematics (DEVM, volume 36)
Access this book
Tax calculation will be finalised at checkout
Other ways to access
About this book
The authors make systematic use of basic facts concerning Lagrange planes and symplectic matrices, and apply some fundamental methods of topological dynamics and ergodic theory. Among the tools used in the analysis, which include Lyapunov exponents, Weyl matrices, exponential dichotomy, and weak disconjugacy, a fundamentalrole is played by the rotation number for linear Hamiltonian systems of general dimension. The properties of all these objects form the basis for the study of several themes concerning linear-quadratic control problems, including the linear regulator property, the Kalman-Bucy filter, the infinite-horizon optimization problem, the nonautonomous version of the Yakubovich Frequency Theorem, and dissipativity in the Willems sense.
The book will be useful for graduate students and researchers interested in nonautonomous differential equations; dynamical systems and ergodic theory; spectral theory of differential operators; and control theory.
Similar content being viewed by others
Keywords
- Linear Hamiltonian systems
- Nonautonomous systems
- Oscillation theory
- Control theory
- Dissipative systems
- Lagrangian flow
- Grassmannian flows
- Kotani theory
- Spectral theory
- Sacker-Sell perturbation theory
- Disconjugacy
- Weak disconjugacy
- Principal solutions
- Rotation number
- Lyapunov exponents
- Lyapunov index
- Exponential dichotomy
- Weyl functions
- Floquet coefficient
- Dynamical spectrum
Table of contents (8 chapters)
Authors and Affiliations
Bibliographic Information
Book Title: Nonautonomous Linear Hamiltonian Systems: Oscillation, Spectral Theory and Control
Authors: Russell Johnson, Rafael Obaya, Sylvia Novo, Carmen Núñez, Roberta Fabbri
Series Title: Developments in Mathematics
DOI: https://doi.org/10.1007/978-3-319-29025-6
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer International Publishing Switzerland 2016
Hardcover ISBN: 978-3-319-29023-2Published: 26 March 2016
Softcover ISBN: 978-3-319-80475-0Published: 25 April 2018
eBook ISBN: 978-3-319-29025-6Published: 25 March 2016
Series ISSN: 1389-2177
Series E-ISSN: 2197-795X
Edition Number: 1
Number of Pages: XXI, 497
Topics: Dynamical Systems and Ergodic Theory, Ordinary Differential Equations, Systems Theory, Control