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"The theory presented in this book arose as a product of a continued collaboration between the two authors during the years 2003-2021. The basis for this collaboration was our common interest in passive linear time-invariant input/state/output systems theory. At the time when this project started O. Staffans was preparing a joint article (Ball and Staffans, 2006) with Prof. J. Ball which, in particular, explored the connections between conservative input/state/output systems theory on one hand and some results in the behavioral theory introduced by J.Willems in the late 80's on the other hand. After extensive discussions on the above approach, comparing it to the theory of passive electrical networks, we understood that this opens up a new direction in the study of passive linear time-invariant systems. We called the new class of systems that arose in this way passive state/signal systems. From the outset it was clear that the notion of passivity with an arbitrary supply rate fits more naturally into the state/signal setting than in the input/state/output setting, and that the standard "diagonal transformation" of Livésic, the Potapov-Ginzburg transformation, and the Redheffer and chain scattering transformations have natural interpretations as transformations between input/output resolvents of different input/state/output representations of a passive state/signal system. We also soon discovered that virtually all the standard control theory notions, such as controllability and observability, minimality, stability, stabilizability, detectability, and well-posedness have natural state/signal counterparts"--
Sommario
1. Introduction and overview; 2. State/signal systems: trajectories, transformations, and interconnections; 3. State/signal systems: dynamic and frequency domain properties; 4. Input/state/output representations; 5. Input/state/output systems: dynamic and frequency domain properties; 6. Bounded input/state/output systems in continuous and discrete time; 7. Bounded state/signal systems in continuous and discrete time; 8. Semi-bounded input/state/output systems; 9. Semi-bounded state/signal systems; 10. Resolvable input/state/output and state/signal nodes; 11. Frequency domain input/state/output systems; 12. Frequency domain state/signal systems; 13. Internally well-posed systems; 14. Well-posed input/state/output systems; 15. Well-posed state/signal systems; Appendix; Operators and analytic vector bundles in H-spaces; References; Index.
Info autore
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.
