Controllability of Singularly Perturbed Linear Time Delay Systems

This monograph provides a comprehensive analysis of the control of singularly perturbed time delay systems. Expanding on the author's previous work on controllability of linear systems with delays in the state and control variables, this volume's comprehensive coverage makes it a valuable addition to the field. Each chapter is self-contained, allowing readers to study them independently or in succession.
After a brief introduction, the book systematically examines properties of different classes of singularly perturbed time delay systems, including linear time-dependent systems with multiple point-wise and distributed state delays. The author then considers more general singularly perturbed systems with state and control delays. Euclidean space controllability for all of these systems is also discussed, using numerous examples from real-life models throughout the text to illustrate the results presented. More technically complicated proofs are presented in separate subsections. The final chapter includes a section dedicated to non-linear time delay systems.
This book is ideal for researchers, engineers, and graduate students in systems science and control theory. Other applied mathematicians and researchers working in biology and medicine will also find this volume to be a valuable resource.

First research monograph devoted to the analysis of the control of singularly perturbed linear time delay systems Brings together and further develops the author's previous research on the topic Presents material in a comprehensive, self-contained manner, allowing for chapters to be studied independently or consecutively

Résumé
"This book is a comprehensive description of known results on the controllability of possibly non-autonomous two-time-scales singularly perturbed control systems with linear dynamics. ... The results are based on a series of papers by the author himself. The proofs given in the book provide more details, and most results are obtained here in a generalized setting ... . All results are richly illustrated by academic and application oriented examples." (Mario Sigalotti, Mathematical Reviews, October, 2022)
The book is rich in content and detailed in proof. One of the biggest features of this book is that theoretical results, obtained in the book, are illustrated by numerous examples ... which is more convenient for readers to read and understand. The book can be helpful for researchers and engineers, working in ... electrical engineering, mechanical and aerospace engineering ... ." (Liping Chen, zbMATH 1472.93014, 2021)

Contenu
Introduction.- Singularly Perturbed Linear Time Delay Systems.- Euclidean Space Output Controllability of Linear Systems with State Delays.- Complete Euclidean Space Controllability of Linear Systems with State and Control Delays.- First-Order Euclidean Space Controllability Conditions for Linear Systems with Small State Delays.- Miscellanies