Nonlinear Time-Delay Systems A Geometric Approach

This brief focuses on the structural properties of nonlinear time-delay systems. It provides a link between coverage of fundamental theoretical properties and advanced control algorithms, as well as suggesting a path for the generalization of the differential geometric approach to time-delay systems .

The brief begins with an introduction to a class of single-input nonlinear time-delay systems. It then focuses on geometric methods treating them and offers a geometric framework for integrability. The book has chapters dedicated to the accessibility and observability of nonlinear time-delay systems, allowing readers to understand the systems in a well-ordered, structured way. Finally, the brief concludes with applications of integrability and the control of single-input time-delay systems.

This brief employs exercises and examples to familiarize readers with the time-delay context. It is of interest to researchers, engineers and postgraduate students who work in the area of nonlinear control systems.

Chapter 1. Introduction.- Chapter 2. Geometric Tools for Time Delay Systems.- Chapter 3. The Geometric Framework – Results on Integrability.- Chapter 4. Accessibility of Nonlinear Time-Delay Systems.- Chapter 5. On the Geometric Interpretation of the Polynomial Lie Bracket.- Chapter 6. Observability.- Chapter 7. Characterization of the Chain Form with Delays.- Chapter 8. Applications of Integrability.- Chapter 9. Control of Single-Input Time Delay Systems.

Claudia Califano is currently an Associate Professor at the Department of Computer, Control, and Management Engineering, University of Rome La Sapienza. In 1998, she received her Ph.D. degree from the University of Rome la Sapienza. She held a post-doctoral position at the Laboratoire des Signaux et Systèmes, CNRS–Supelec, Gif-sur-Yvette, before returning to the University of Rome la Sapienza as an Assistant Professor in 2000. She has held several positions as Visiting Professor in particular at  Ecole Centrale de Nantes and Polytechnique Nantes. She has authored and co-authored numerous publications, including journal articles, conference papers and two chapters in books. She is a senior member of the IEEE Control Systems Society, a member of the IEEE CSS  Technical Committee Nonlinear Systems and Control and the IFAC Technical Committee Nonlinear Control Systems, and an Associate Editor for the IMA Mathematical Control and Information Journal.

Claude Moog gained his M.Sc. in Automatic Control from the University of Franche-Comté and his Ph.D. from the University of Nantes, in 1978 and 1981, respectively. After an Assistant Professor position at Ecole Centrale de Lyon, he entered as a full-time researcher at CNRS in 1983. He was awarded the title of IEEE Fellow in 2007 and Corresponding Member of the Mexican Academy of Sciences in 2011. He has published over 90 journal articles, over 150 international conference papers and 4 books. He is a member of several international committees and has acted as an Associate Editor of multiple journals, including IEEE Transactions on Automatic Control.