Preliminaries

Abstract

The aim of this book is to study a new mathematical tool named differential linear matrix inequality (DLMI) which, as the denomination indicates, is a natural generalization of the well-known linear matrix inequality (LMI) that has had an important impact in systems and control theory. With this goal in mind, this book focuses on the following main aspects: the general context on which DLMI can be successfully applied, numerical determination of a solution whenever it exists, and control and filtering design problems involving sampled-data systems. The first and the third aspects are related in the sense that sampled-data control systems have already been identified as a research area, where DLMIs can be applied with positive impact on both theoretical and numerical viewpoints. The second one is crucial, in order to make DLMIs really amenable to users dealing with control system analysis and design. This chapter provides a brief discussion on the importance and usefulness of DLMIs, a brief description of the content and structure of each chapter, and the main notation.