Linear State/Signal Systems

Damir Z. Arov

ISBN 10: 1316519678 / ISBN 13: 9781316519677

Edité par Cambridge University Press, 2022

A propos de cet article

Druck auf Anfrage Neuware - Printed after ordering - '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'--.

N° de réf. du vendeur 9781316519677

Détails bibliographiques

• Titre: Linear State/Signal Systems
• Éditeur: Cambridge University Press
• Date de parution: 2022
• Langue: anglais
• ISBN à 10 chiffres: 1316519678
• ISBN à 13 chiffres: 9781316519677
• Reliure: Buch
• État de l'article: Neu
• Dimensions: 250 L x 175 H x 60 P (en millimètres) 250 millimètres de largeur par 175 millimètres de hauteur par 60 millimètres de profondeur
• Poids: 1947 grammes

A propos de ce titre

Synopsis

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.

À propos des auteurs

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.