Nonautonomous Linear Hamiltonian Systems: Oscillation, Spectral Theory and Control - Developments in Mathematics 36 (Hardback)Russell Johnson (author), Rafael Obaya (author), Sylvia Novo (author), Carmen Nunez (author), Roberta Fabbri (author)
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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.
Publisher: Springer International Publishing AG
Number of pages: 497
Weight: 937 g
Dimensions: 235 x 155 x 29 mm
Edition: 1st ed. 2016
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