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Nonautonomous Linear Hamiltonian Systems: Oscillation, Spectral Theory and Control (Hardcover, 1st ed. 2016)
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Nonautonomous Linear Hamiltonian Systems: Oscillation, Spectral Theory and Control (Hardcover, 1st ed. 2016)
Series: Developments in Mathematics, 36
Expected to ship within 10 - 15 working days
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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.
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