Download E-books Nonautonomous Linear Hamiltonian Systems: Oscillation, Spectral Theory and Control (Developments in Mathematics) PDF

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

This monograph comprises an in-depth research of the dynamics given by way of a linear Hamiltonian approach of normal measurement with nonautonomous bounded and uniformly non-stop coefficients, with no different preliminary assumptions on time-recurrence. specific realization is given to the oscillation houses of the suggestions in addition to to a spectral idea acceptable for such platforms. The booklet includes extensions of effects that are renowned while the coefficients are independent or periodic, in addition to within the nonautonomous two-dimensional case. even if, a considerable a part of the speculation awarded here's new even in these a lot less complicated situations.
The authors make systematic use of simple evidence bearing on Lagrange planes and symplectic matrices, and practice a few primary tools of topological dynamics and ergodic idea. one of the instruments utilized in the research, which come with Lyapunov exponents, Weyl matrices, exponential dichotomy, and vulnerable disconjugacy, a primary position is performed by means of the rotation quantity for linear Hamiltonian platforms of common measurement. The houses of these types of gadgets shape the foundation for the learn of a number of subject matters referring to linear-quadratic keep watch over difficulties, together with the linear regulator estate, the Kalman-Bucy filter out, the infinite-horizon optimization challenge, the nonautonomous model of the Yakubovich Frequency Theorem, and dissipativity within the Willems sense.
The ebook may be priceless for graduate scholars and researchers attracted to nonautonomous differential equations; dynamical platforms and ergodic idea; spectral thought of differential operators; and regulate theory.

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