Linear State/Signal Systems

┬╖ Encyclopedia of Mathematics and its Applications рдкреБрд╕реНрддрдХ 183 ┬╖ Cambridge University Press
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The authors explain in this work a new approach to observing and controlling linear systems whose inputs and outputs are not fixed in advance. They cover a class of linear time-invariant state/signal system that is general enough to include most of the standard classes of linear time-invariant dynamical systems, but simple enough that it is easy to understand the fundamental principles. They begin by explaining the basic theory of finite-dimensional and bounded systems in a way suitable for graduate courses in systems theory and control. They then proceed to the more advanced infinite-dimensional setting, opening up new ways for researchers to study distributed parameter systems, including linear port-Hamiltonian systems and boundary triplets. They include the general non-passive part of the theory in continuous and discrete time, and provide a short introduction to the passive situation. Numerous examples from circuit theory are used to illustrate the theory.

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Damir Z. Arov is Professor in Mathematics at South-Ukrainian National Pedagogical University in Odessa. He introduced the notion of ╬╡-entropy (predating the KolmogorovтАУSinai entropy), is one of the authors behind the AdamyanтАУArovтАУKrein theory used in HтИЮ control, and developed passive systems theory and the theory of J-contractive matrix-valued functions. He has written approximately 200 journal articles and co-authored three monographs with Professor Harry Dym. Professor Arov, is an honorary doctor from ├Еbo Akademi University, Finland, and has received the Krein prize from the Ukrainian Academy of Sciences.

Olof J. Staffans is Professor Emeritus in Mathematics at ├Еbo Akademi University in Finland. He is the author of Well-Posed Linear Systems (Cambridge, 2005) and a co-author of Volterra Integral and Functional Equations (Cambridge, 1990), and has published more than 100 journal articles. He is a fellow of the American Mathematical Society and a member of the Finnish Society of Sciences and Letters from which he received the E. J. Nystr├╢m award.

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