Linear Operators and Linear Systems An Analytical Approach to Control Theory
Linear Operators and Linear Systems: An Analytical Approach to Control Theory by Jonathan R. Partington, published by Cambridge University Press on March 15, 2004, spans 166 pages and is presented in English. This book introduces the relationship between operator theory and linear systems theory, focusing on linear systems as causal shift-invariant operators within a Hilbert space of signals. It covers a range of mathematical topics, including Hardy spaces, closed operators, and the commutant lifting theorem, making it suitable for courses in functional analysis.
Readers will find a blend of theoretical and practical applications, with discussions on partial differential equations, stability and stabilization of linear systems, and power signal spaces. The book also addresses delay systems from an input/output perspective, making it relevant for students of analysis and graduate students in applied mathematics or engineering. This edition serves as a comprehensive resource for those looking to explore the mathematical foundations of systems and control theory.
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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.
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