Linear Operators and Linear Systems
An Analytical Approach to Control Theory

This book presents an introduction to the common ground between operator theory and linear systems theory.

Jonathan R. Partington (Author)

9780521546195, Cambridge University Press

Paperback, published 15 March 2004

178 pages, 6 b/w illus. 101 exercises
22.9 x 16 x 1.1 cm, 0.32 kg

'The author has succeeded in covering a large amount of material in rather few pages. this volume gives a good introduction to the theory of infinite-dimensional systems, although mostly for those described by delay differential equations (rather than partial differential equations). It also contains much material that should be of interest to engineers and mathematicians. there are numerous examples and exercises, ranging from concrete to abstract, which contribute to delineate the natural limits of some of the results.' Zentralblatt MATH

Linear systems can be regarded as a causal shift-invariant operator on a Hilbert space of signals, and by doing so this book presents an introduction to the common ground between operator theory and linear systems theory. The book therefore includes material on pure mathematical topics such as Hardy spaces, closed operators, the gap metric, semigroups, shift-invariant subspaces, the commutant lifting theorem and almost-periodic functions, which would be entirely suitable for a course in functional analysis; at the same time, the book includes applications to partial differential equations, to the stability and stabilization of linear systems, to power signal spaces (including some recent material not previously available in books), and to delay systems, treated from an input/output point of view. Suitable for students of analysis, this book also acts as an introduction to a mathematical approach to systems and control for graduate students in departments of applied mathematics or engineering.

1. Operators and Hardy spaces
2. Closed operators
3. Shift-invariance and causality
4. Stability and stabilization
5. Spaces of persistent signals
6. Delay systems.

Subject Areas: Applied mathematics [PBW], Functional analysis & transforms [PBKF]