In September 1998, during the 'International Workshop on Analysis and Vibrat ing Systems' held in Canmore, Alberta, Canada, it was decided by a group of participants to honour Peter Lancaster on the occa...
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Discrete-time systems arise as a matter of course in modelling biological or economic processes. For systems and control theory they are of major importance, particularly in connection with digital control application...
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ISBN:
(数字)9783034884990
ISBN:
(纸本)9783764350123;9783034896511
Discrete-time systems arise as a matter of course in modelling biological or economic processes. For systems and control theory they are of major importance, particularly in connection with digital control applications. If sampling is performed in order to control periodic processes, almost periodic systems are obtained. This is a strong motivation to investigate the discrete-time systems with time-varying coefficients. This research monograph contains a study of discrete-time nodes, the discrete counterpart of the theory elaborated by Bart, Gohberg and Kaashoek for the continuous case, discrete-time Lyapunov and Riccati equations, discrete-time Hamiltonian systems in connection with input-output operators and associated Hankel and Toeplitz operators. All these tools aim to solve the problems of stabilization and attenuation of disturbances in the framework of H2- and H-control theory. The book is the first of its kind to be devoted to these topics and consists mainly of original, recently obtained results.
This open access book gives a systematic introduction into the spectral theory of differential operators on metric graphs. Main focus is on the fundamental relations between the spectrum and the geometry of the underl...
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ISBN:
(数字)9783662678725
ISBN:
(纸本)9783662678701
This open access book gives a systematic introduction into the spectral theory of differential operators on metric graphs. Main focus is on the fundamental relations between the spectrum and the geometry of the underlying graph.;The book has two central themes: the;and;.;The;is relating the spectrum to the set of periodic orbits and is comparable to the celebrated Selberg and Chazarain-Duistermaat-Guillemin-Melrose trace formulas. Unexpectedly this formula allows one to construct non-trivial crystalline measures and Fourier quasicrystals solving one of the long-standing problems in Fourier analysis. The remarkable story of this mathematical odyssey is presented in the first part of the book.;To solve the;for Schrödinger operators on metric graphs the magnetic boundary control method is introduced. Spectral data depending on the magnetic flux allow one to solve the inverse problem in full generality, this means to reconstruct not only the potential on a given graph, but also the underlying graph itself and the vertex conditions.;The book provides an excellent example of recent studies where the interplay between different fields like operatortheory, algebraic geometry and number theory, leads to unexpected and sound mathematical results. The book is thought as a graduate course book where every chapter is suitable for a separate lecture and includes problems for home studies. Numerous illuminating examples make it easier to understand new concepts and develop the necessary intuition for further studies.
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