S-Variable Approach to LMI-Based Robust Control - Ebihara, Yoshio (Springer, 2015)
At the end of 1990s, we discovered with enthusiasm the publication by Mauricio C. de Oliveira, Jacques Bernussou, and José C. Geromel concerning a “New Discrete Time Stability Condition.” Since then, we have dedicated most of our attention to understanding and applying the underlying powerful methodology. We have extended the results in many directions and witnessed major interest of our colleagues for these extensions. The technique is now widely used but never was completely formalized. Because of that, it has been sometimes missused or missinterpreted, some central issues have not been clarified, and there is not even a unique denomination for it. In this book, we decide to call that methodology the S-variable approach, following the denomination S-procedure that is a powerful tool in dealing with constrained inequality conditions. We explain this choice, expose in details our understanding of it, and provide important robust control results related to it...