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This book is primarily a research monograph that presents in a unified man ner some recent research on a class of hybrid dynamical systems (HDS). The book is intended both for researchers and advanced postgraduate stu dents working in the areas of control engineering, theoretical computer science, or applied mathematics and with an interest in the emerging field of hybrid dynamical systems. The book assumes competence in the basic mathematical techniques of modern control theory. The material presented in this book derives from a period of fruitful research collaboration between the authors that began in 1994 and is still ongoing. Some of the material contained herein has appeared as isolated results in journal papers and conference proceedings. This work presents this material in an integrated and coherent manner and also presents many new results. Much of the material arose from joint work with students and colleagues, and the authors wish to acknowledge the major contributions made by Ian Petersen, Efstratios Skafidas, Valery Ugrinovskii, David Cook, Iven Mareels, and Bill Moran. There is currently no precise definition of a hybrid dynamical system; however, in broad terms it is a dynamical system that involves a mixture of discrete-valued and continuous-valued variables. Since the early 1990s, a bewildering array of results have appeared under the umbrella of HDS, ranging from the analysis of elementary on-off control systems to sophis ticated mathematical logic-based descriptions of large real-time software systems.

Hybrid Dynamical Systems

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thank you for the invitation to come here and speak and welcome everyone so how many of you have taken a course that teaches you hybrid systems okay more people coming how many of you have taken a course that teaches you model predictor control and I guess my next answer was if you took a course with hybrid systems and model predator control but maybe the answer is clear so today I'm gonna be talking about those two things and so I wanted to start with what are hybrid systems and I wanted to show you some of the applications of hybrid system this is hybrid because this manipulators which could be robots and maybe it's hard to see where there are little dots that make contact with these object as they move along and as they move along we would like the contact to clear at the same time so that this object doesn't get disturb because it could be a ball and it could be rolling if you impac