Robust control of infinite dimensional systems. Frequency domain methods
In this book, which can be seen as a sequel to that of \textit{B. Francis} [this series, No. 88 (1987; Zbl 0624.93003)], the authors present their development of \(H^\infty\)-control theory for infinite-dimensional systems. While the operator theoretic approach played a fundamental role from the beginning of the development of \(H^\infty\)-theory, it was recently shunted aside by the state space approach whose advantage is, in the finite-dimensional case, direct and straightforward computation of controllers. This ceases to be the case for infinite-dimensional systems and here the conceptual elegance of the operator theoretic approach stands out. The authors, major contributors to the development of this approach, have presented in this book a concise and pretty description of the basic problems and their solutions, as well as the applications of the theory to two ``benchmark'' problems, a flexible beam problem and an unstable delay system. Special features in this book are the skew Toeplitz approach developed by the authors and the actual computation of optimal controllers for some infinite-dimensional problems by solving a system of linear equations. All in all, an important contribution to the growing literature on the subject.
scientific article; zbMATH DE number 827356