This book is aimed at mathematicians, scientists, and engineers, studying models that involve a discontinuity, or studying the theory of nonsmooth systems for its own sake. It is divided in two complementary courses: piecewise smooth flows and maps, respectively. Starting from well known theoretical results, the authors bring the reader into the latest challenges in the field, going through stability analysis, bifurcation, singularities, decomposition theorems and an introduction to kneading theory. Both courses contain many examples which illustrate the theoretical concepts that are introduced.

This volume contains extended abstracts outlining selected talks and other selected presentations given by participants throughout the "Intensive Research Program on Advances in Nonsmooth Dynamics 2016", held at the Centre de Recerca Matematica (CRM) in Barcelona from February 1st to April 29th, 2016. They include brief research articles reporting new results, descriptions of preliminary work or open problems, and outlines of prominent discussion sessions. The articles are all the result of direct collaborations initiated during the research program. The topic is the theory and applications of Nonsmooth Dynamics. This includes systems involving elements of: impacting, switching, on/off control, hybrid discrete-continuous dynamics, jumps in physical properties, and many others. Applications include: electronics, climate modeling, life sciences, mechanics, ecology, and more. Numerous new results are reported concerning the dimensionality and robustness of nonsmooth models, shadowing variables, numbers of limit cycles, discontinuity-induced bifurcations and chaos, determinacy-breaking, stability criteria, and the classification of attractors and other singularities. This material offers a variety of new exciting problems to mathematicians, but also a diverse range of new tools and insights for scientists and engineers making use of mathematical modeling and analysis. The book is intended for established researchers, as well as for PhD and postdoctoral students who want to learn more about the latest advances in these highly active areas of research.

The tracking/rejection of periodic signals constitutes a wide field of research in the control theory and applications area. Repetitive Control has proven to be an efficient way to face this topic. However, in some applications the frequency of the reference/disturbance signal is time-varying or uncertain. This causes an important performance degradation in the standard Repetitive Control scheme. This book presents some solutions to apply Repetitive Control in varying frequency conditions without loosing steady-state performance. It also includes a complete theoretical development and experimental results in two representative systems. The presented solutions are organized in two complementary branches: varying sampling period Repetitive Control and High Order Repetitive Control. The first approach allows dealing with large range frequency variations while the second allows dealing with small range frequency variations. The book also presents applications of the described techniques to a Rota-magnet plant and to a power active filter device.