Nonautonomous Linear Hamiltonian Systems: Oscillation, Spectral Theory and Control
Authors: Johnson, R., Obaya, R., Novo, S., Núñez, C., Fabbri, R.
 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 timevarying coefficients
 Applies known results of the theory of periodic Hamiltonian systems to the general nonautonomous case and presents various new properties
Buy this book
 About this book

This monograph contains an indepth 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 timerecurrence. 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 twodimensional 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 fundamental role 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 linearquadratic control problems, including the linear regulator property, the KalmanBucy filter, the infinitehorizon 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.
Buy this book
Recommended for you
Bibliographic Information
 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
 Series Volume
 36
 Copyright
 2016
 Publisher
 Springer International Publishing
 Copyright Holder
 Springer International Publishing Switzerland
 eBook ISBN
 9783319290256
 DOI
 10.1007/9783319290256
 Hardcover ISBN
 9783319290232
 Series ISSN
 13892177
 Edition Number
 1
 Number of Pages
 XXI, 497
 Topics