Linear Operators and Linear Systems: An Analytical Approach to Control Theory: 60 (London Mathematical Society Student Texts, Series Number 60)
Cambridge University Press
Edition: Illustrated, 3/22/2004
EAN 9780521837347, ISBN10: 0521837340
Hardcover, 178 pages, 22.9 x 15.2 x 1.5 cm
Language: English
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.