Science/Engineering Functional Analysis and Linear Control Theory (Mathematics in Science and Engineering): J. R. Leigh (0124418805)

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Functional Analysis and Linear Control Theory (Mathematics in Science and Engineering): J. R. Leigh

Functional analysis provides a concise conceptual framework for linear control theory. This self-contained text, geared toward engineering students, demonstrates the subject's unity. A wide range of powerful theorems illustrates inner product spaces; instability, controllability, and observability; minimum norm and time control; and distributed systems. 1980 edition.

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This short book presents an overview of mathematical results (i.e. proofs) concerning existence and uniqueness for linear state space methods of control theory. A good prerequisite would be that you already know either some functional analysis or some state space control theory, and you want to see how these two fields work together. The author covers topological, Banach, and Hilbert spaces and their applicability to optimal controllers via typical control theory cost functions. Some material on distributed systems is presented at the end. The few worked examples are trivial in nature compared to typical control theory books, but this is in keeping with the abstract mathematical nature of the book. Since this book is a 1980 edition, many addition interesting results are presumably known today (2008), but this book seems to be a good starting point. For a less proof oriented book, still done with somewhat of a mathematical bent and with many more examples, consider the masterpiece, Modern Control Theory, by Brogan. Happy controlling.

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