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Nonautonomous Linear Hamiltonian Systems: Oscillation, Spectral Theory and Control: Developments in Mathematics, cartea 36

Autor Russell Johnson, Rafael Obaya, Sylvia Novo, Carmen Núñez, Roberta Fabbri
en Limba Engleză Hardback – 26 mar 2016
This monograph contains an in-depth analysis of the dynamics given by a linear Hamiltonian system of general dimension with nonautonomous bounded and uniformly continuous coefficients, without other initial assumptions on time-recurrence. Particular attention is given to the oscillation properties of the solutions as well as to a spectral theory appropriate for such systems. The book contains extensions of results which are well known when the coefficients are autonomous or periodic, as well as in the nonautonomous two-dimensional case. However, a substantial part of the theory presented here is new even in those much simpler situations.

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.
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Specificații

ISBN-13: 9783319290232
ISBN-10: 3319290231
Pagini: 390
Ilustrații: XXI, 497 p.
Dimensiuni: 155 x 235 x 34 mm
Greutate: 0.9 kg
Ediția:1st ed. 2016
Editura: Springer International Publishing
Colecția Springer
Seria Developments in Mathematics

Locul publicării:Cham, Switzerland

Public țintă

Research

Cuprins

Nonautonomouslinear Hamiltonian systems.- The rotation number and the Lyapunov index forreal nonautonomous linear Hamiltonian systems.- The Floquet coeffcient fornonautonomous linear Hamiltonian systems: Atkinson problems.- The Weylfunctions.- Weak disconjugacy for linear Hamiltonian systems.- Nonautonomouscontrol theory. Linear regulator problem and the Kalman-Bucy filter.-Nonautonomous control theory. A general version of the Yakubovich FrequencyTheorem.- Nonautonomous control theory. Linear-quadratic dissipative controlprocesses.- Index.- References

Textul de pe ultima copertă

This monograph contains an in-depth analysis of the dynamics given by a linear Hamiltonian system of general dimension with nonautonomous bounded and uniformly continuous coefficients, without other initial assumptions on time-recurrence. Particular attention is given to the oscillation properties of the solutions as well as to a spectral theory appropriate for such systems. The book contains extensions of results which are well known when the coefficients are autonomous or periodic, as well as in the nonautonomous two-dimensional case. However, a substantial part of the theory presented here is new even in those much simpler situations.

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.

Caracteristici

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 Hamiltoniansystems to the general nonautonomous case and presents various new properties