Differential Linear Matrix Inequalities

This book is entirely devoted to sampled-data control systems analysis and design from a new point of view, which has at its core a mathematical tool named Differential Linear Matrix Inequality - DLMI, a natural generalization of Linear Matrix Inequality - LMI, that had an important and deep impact on systems and control theory almost thirty years ago. It lasts until now. It is shown that the DLMI is well adapted to deal with the important class of sampled-data control systems in both theoretical and numerical contexts. All design conditions are expressed by convex programming problems, including when robustness against parameter uncertainty is assessed and imposed through state feedback control.
Special attention is given to filter, dynamic output feedback and model predictive control design, as well as nonlinear systems of Lur'e class and Markov jump linear systems.
The subject is treated with mathematical rigor, at the same time, trying to keep the reading agreeable and fruitful for colleagues and students. To this respect, the book contains together with the theoretical developments, many solved illustrative examples and the formulation of some open problems that could be faced and hopefully solved by interested readers.

Describes a new mathematical tool named differential linear matrix inequality (DLMI) and its applications Presents and discusses a numerical determination of a solution whenever it exists Includes coverage of Control and filtering design problems involving sampled-data systems

Auteur

José C. Geromel received the Bs. and Ms. degrees in Electrical Engineering from University of Campinas - UNICAMP, Brazil, in 1975 and 1976, respectively, and the Docteur d Etat degree from University Paul Sabatier - LAAS/CNRS, Toulouse, France, in 1979. He joined the School of Electrical and Computer Engineering at UNICAMP in 1975, where he is a full professor of Control Systems Analysis and Design. In 1987, he held a visiting professor position at Polytechnic Institute of Milan, Milan, Italy. He has been a member of the Editorial Board of International Journal of Robust and Nonlinear Control and Associate Editor of European Journal of Control and Nonlinear Analysis: Hybrid Systems. He was awarded in 1994 and 2014 the Zeferino Vaz Award for his teaching and research activities at UNICAMP and, in 2007, the Scopus Award jointly awarded by Elsevier and CAPES / Brazil. Since 1991 he has been a Fellow 1-A of the Brazilian National Council for Scientific and Technological Development-CNPq. Since 1998 he has been a member of the Brazilian Academy of Science.

In 1999, he was named Chevalier dans l Ordre des Palmes Acad emiques by the French Minister of National Education. In 2010, he received the Docteur Honoris Causa degree from University Paul Sabatier, Toulouse, France and was named a member of the Brazilian Order of Scientific Merit by the President of the Federative Republic of Brazil. In 2011, he was named Distinguished Lecturer by the IEEE Control Systems Society. In 2018, he was promoted to Gr a-Cruz of the Brazilian Order of Scientific Merit.

He is co-author of the books Control Theory and Design - with P. Colaneri and A. Locatelli, Academic Press, 1997, An alise Linear de Sistemas Din amicos, (in Portuguese), - with A. G. B. Palhares, Edgard Blucher, 2004, Controle Linear de Sistemas Din amicos, (in Portuguese), - with R. H. Korogui, Edgard Blucher, 2011, and An alise Linear de Sinais, (in Portuguese), - with G. S. Deaecto, Edgard Blucher, 2019.

His research papers and books have received so far 15, 526 citations (h = 59) in Google Scholar and 8, 722 citations (h = 46) in Web of Science platforms.

Résumé

"The subject of the book is well expressed by its title. The book is very organized. Each chapter begins by an introductory section and ends by a section of bibliography notes. The book offers both mathematical rigor and attractiveness for the reader ... ." (Henri Bourlès, zbMATH 1529.93001, 2024)

Contenu

Preliminaries.- Differential linear matrix inequalities.- Sampled-data control systems.- H2 filtering and control.- H filtering and control.- Markov jump linear systems.- Nonlinear systems control.- Model predictive control.- Numerical experiments.