Titlebook: Nonautonomous Linear Hamiltonian Systems: Oscillation, Spectral Theory and Control; Russell Johnson,Rafael Obaya,Roberta Fabbri Book 2016

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The Weyl Functions,ze to the n-dimensional Schrödinger equation a famous inequality (obtained in the scalar case by Moser (1980) and by Deift and Simon (1983)) involving the rotation number and its derivative. The chapter ends with a description of a scenario in which the convergence of the Weyl functions is uniform.

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,Nonautonomous Control Theory: Linear Regulator Problem and the Kalman–Bucy Filter,miltonian systems are used to produce direct proofs of some basic results, including the asymptotic limit and the stability properties of the error covariance matrix, and the Hurwitz property at . of the error propagation system.

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Nonautonomous Control Theory: Linear-Quadratic Dissipative Control Processes, occurrence of uniform weak disconjugacy permits one to establish some weaker equivalences, formulated in terms of one of the principal functions. Some dynamical conditions ensuring the dissipativity of the linear-quadratic problem are also given without assuming the controllability property. The op

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Book 2016 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

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