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 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 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.
