This new text/reference is an excellent resource for the foundations and applications of control theory and nonlinear dynamics. All graduates, practitioners, and professionals in control theory, dynamical systems, perturbation theory, engineering, physics and nonlinear dynamics will find the book a rich source of ideas, methods and applications. With its careful use of examples and detailed development, it is suitable for use as a self-study/reference guide for all scientists and engineers.

This research monograph deals with optimal periodic control problems for systems governed by ordinary and functional differential equations of retarded type. Particular attention is given to the problem of local properness, i.e. whether system performance can be improved by introducing periodic motions. Using either Ekeland's Variational Principle or optimization theory in Banach spaces, necessary optimality conditions are proved. In particular, complete proofs of second-order conditions are included and the result is used for various versions of the optimal periodic control problem....

This volume contains the lectures presented at the workshop on "Advances in Mathematical Systems Theory," held on the island of Borkum, Germany (April 20-23, 1999). The book will be of interest to graduate students and researchers interested in control theory and mathematical systems theory, who will find in-depth analysis and presentations from diverse perspectives interacting in this lively area. The editors are proud to dedicate this volume to Diederich Hinrichsen on the occasion of his 60th birthday in acknowl- edgment of his major contributions to linear systems theory and control theory...

A book is never the sole accomplishment of the authors. It is built on the foun- dation of established mathematics, and it benefits from current developments within the mathematical community. Many colleagues have contributed ideas, comments, and corrections to this volume. There are, first of all, our students C. Bauer, G. Grammel, 1. Greger, S. Grtinvogel, G. Hackl, and D. Szolnoki in Augs- burg, and E. Joseph, R.-G. Lai, S. Lin, C.-M. Ou, and H. Wang in Ames. We have received comments from, among others, L. Arnold, V. Ayala, K. Grasse, D. Hinrichsen, R. Johnson, Y. Latushkin, J.L. Massera,...

The articles in this volume cover the different facets of the mathematical theory of dynamical systems. Topics range from topological foundations through invariant manifolds, decoupling, perturbations and computations to control theory.