Yutaka Yamamoto

Provides a treatment of analytical methods of applied mathematics. It starts with a review of the basics of vector spaces and brings the reader to an advanced discussion of applied mathematics, including the latest applications to systems and control theory. The text is designed to be accessible to those not familiar with the material and useful to working scientists, engineers, and mathematics students. The author provides the motivations of definitions and the ideas underlying proofs but does not sacrifice mathematical rigour. From Vector Spaces to Function Spaces presents an easily-accessible discussion of analytical methods of applied mathematics from vector spaces to distributions, Fourier analysis, and Hardy spaces with applications to system theory; an introduction to modern functional analytic methods to better familiarize readers with basic methods and mathematical thinking; and an understandable yet penetrating treatment of such modern methods and topics as function spaces and distributions, Fourier and Laplace analyses, and Hardy spaces.

This book presents new computational tools for the H8 control of distributed parameter systems in which transfer functions are considered as input-output descriptions for the plants to be controlled. The emphasis is on the computation of the controller parameters and reliable implementation. The authors present recent studies showing that the simplified skew Toeplitz method is applicable to a wide class of systems, supply detailed examples from systems with time delays and various engineering applications, and discuss reliable implementation of the controller, complemented by a software based on MATLAB®. Frequency Domain Techniques for H8 Control of Distributed Parameter Systems is intended for advanced undergraduate and early graduate students interested in robust control of distributed parameter systems—time delay systems—as well as researchers and engineers working in related fields. It can be used in the following courses: Introduction to Robust Control with Applications to Distributed Parameter Systems and Introduction to Robust Control with Applications to Time Delay Systems.