Differential Linear Matrix Inequalities

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