Linear State/Signal Systems

Damir Z. Arov, Olof J. Staffans

• Publisher: Cambridge University Press
• Year: 2022
• Print ISBN:
  9781316519677
• eBook ISBN:
  9781009021739
• Topic: Mathematics
• Subtopic: Mathematics General
• Index: Mathematics

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.

Table of contents

• Cover
• Half-title page
• Series page
• Title page
• Copyright page
• Contents
• Preface
• List of Notations
• 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 A Operators and Analytic Vector Bundles in H-Spaces
• References
• Index