Linear State/Signal Systems (Encyclopedia of Mathematics and its Applications, Series Number 183)

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.

Damir Z. Arov is Professor in Mathematics at South-Ukrainian National Pedagogical University in Odessa. He introduced the notion of ε-entropy (predating the Kolmogorov–Sinai entropy), is one of the authors behind the Adamyan–Arov–Krein theory used in H∞ 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 Åbo Akademi University, Finland, and has received the Krein prize from the Ukrainian Academy of Sciences.

Olof J. Staffans is Professor Emeritus in Mathematics at Åbo 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. Nyström award.