An Introduction to Hybrid Dynamical Systems

This work is about dynamical systems that are "hybrid" in the sense that they contain both continuous and discrete state variables. Recently there has been increased research interest in the study of the interaction between discrete and continuous dynamics. The present volume provides an attempt to bring together concepts and methods dealing with hybrid systems from various areas, and to look at these from a unified perspective. The authors have chosen a mode of exposition that is largely based on illustrative examples rather than on the abstract theorem-proof format, largely because the systematic study of hybrid systems is still in its infancy. The examples are taken from many different application areas, ranging from power converters to communication protocols and from chaos theory to mathematical finance. The book should be of interest to scientists from a wide range of disciplines, including: computer science, control theory, dynamical system theory, systems modelling and simulation, and operations research.