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Nonautonomous Linear Hamiltonian Systems: Oscillation, Spectral Theory and Control

Part of the Developments in Mathematics Book Series (volume 36)

DOI: 10.1007/978-3-319-29025-6

ISBN: 978-3-319-29023-2

Publisher: Springer International Publishing - Springer Journals

Mar 26, 2016

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Chapter 1Nonautonomous Linear Hamiltonian Systems

Johnson, Russell; Obaya, Rafael; Novo, Sylvia; Núñez, Carmen; Fabbri, Roberta

Pages: 1 –75

[In this chapter, the framework of analysis of the book is described, and the many foundational facts required for this analysis are stated. The first two sections present fundamental notions and properties of topological dynamics and ergodic theory, as well as basic results concerning spaces of...
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Chapter 2The Rotation Number and the Lyapunov Index for Real Nonautonomous Linear Hamiltonian Systems

Johnson, Russell; Obaya, Rafael; Novo, Sylvia; Núñez, Carmen; Fabbri, Roberta

Pages: 77 –124

[In this chapter, two objects are introduced and analyzed, namely the rotation number and the Lyapunov index for a family of nonautonomous linear 2n-dimensional Hamiltonian systems. They depend on the choice of a fixed ergodic measure on the space Ω (whose elements determine the different systems...
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Chapter 3The Floquet Coefficient for Nonautonomous Linear Hamiltonian Systems: Atkinson Problems

Johnson, Russell; Obaya, Rafael; Novo, Sylvia; Núñez, Carmen; Fabbri, Roberta

Pages: 125 –179

[Let a family of linear Hamiltonian systems determined by a coefficient matrix H be perturbed as to obtain \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs}...
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Chapter 4The Weyl Functions

Johnson, Russell; Obaya, Rafael; Novo, Sylvia; Núñez, Carmen; Fabbri, Roberta

Pages: 181 –248

[The main goal of this chapter is the analysis of the limiting qualitative behavior as the (real or complex) parameter \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy}...
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Chapter 5Weak Disconjugacy for Linear Hamiltonian Systems

Johnson, Russell; Obaya, Rafael; Novo, Sylvia; Núñez, Carmen; Fabbri, Roberta

Pages: 249 –328

[The analysis of nonautonomous linear Hamiltonian systems with the disconjugacy property is a classical branch of the theory of linear ODEs. One of the most interesting consequences of this property is the existence of principal functions, which constitute an extension of the concept of Weyl...
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Chapter 6Nonautonomous Control Theory: Linear Regulator Problem and the Kalman–Bucy Filter

Johnson, Russell; Obaya, Rafael; Novo, Sylvia; Núñez, Carmen; Fabbri, Roberta

Pages: 329 –365

[Two goals will be achieved in this chapter. The first one concerns the feedback stabilization problem for a nonautonomous linear control system: the stabilizing feedback control is determined by formulating and solving an infinite horizon linear regulator problem. The minimizing pairs for the...
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Chapter 7Nonautonomous Control Theory: A General Version of the Yakubovich Frequency Theorem

Johnson, Russell; Obaya, Rafael; Novo, Sylvia; Núñez, Carmen; Fabbri, Roberta

Pages: 367 –418

[This chapter is focussed on a nonautonomous version of the well-known Yakubovich Frequency Theorem, which was originally formulated for linear control systems x′ = A(t) x + B(t) u with time-periodic coefficients. The extension of this theorem to the nonautonomous category is formulated in terms...
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Chapter 8Nonautonomous Control Theory: Linear-Quadratic Dissipative Control Processes

Johnson, Russell; Obaya, Rafael; Novo, Sylvia; Núñez, Carmen; Fabbri, Roberta

Pages: 419 –486

[This chapter presents an analysis of the normal or strict Willems dissipativity property of a family of linear-quadratic (LQ) control problems, which are described by time-dependent linear control systems and time-dependent quadratic supply rates. These problems give rise in a natural way to a...

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