Hybrid systems describe the interaction of software, described by finite models such as finite-state machines, with the physical world, described by infinite models such as differential equations. This book addresses problems of verification and controller synthesis for hybrid systems. Although these problems are very difficult to solve for general hybrid systems, several authors have identified classes of hybrid systems that admit symbolic or finite models. The novelty of the book lies on the systematic presentation of these classes of hybrid systems along with the relationships between the hybrid systems and the corresponding symbolic models. To show how the existence of symbolic models can be used for verification and controller synthesis, the book also outlines several key results for the verification and controller design of finite systems. Several examples illustrate the different methods and techniques discussed in the book.

Hybrid systems describe the interaction of software, described by finite models such as finite-state machines, with the physical world, described by infinite models such as differential equations. This book addresses problems of verification and controller synthesis for hybrid systems. Although these problems are very difficult to solve for general hybrid systems, several authors have identified classes of hybrid systems that admit symbolic or finite models. The novelty of the book lies on the systematic presentation of these classes of hybrid systems along with the relationships between the hybrid systems and the corresponding symbolic models. To show how the existence of symbolic models can be used for verification and controller synthesis, the book also outlines several key results for the verification and controller design of finite systems. Several examples illustrate the different methods and techniques discussed in the book.

This volume contains the proceedings of the 12th International Conference on Hybrid Systems Computation and Control (HSCC 2009) held in San Francisco, CaliforniaduringApril13-15,2009. Theannualconferenceonhybridsystems- cuses on researchin embedded, reactive systems involving the interplay between discrete switching and continuous dynamics. HSCC is a forum for academic and industrial researchers and practitioners to exchange information on the latest advancements, both practical and theoretical, in the design, analysis, control, optimization, and implementation of hybrid systems. HSCC 2009 was the 12th in a series of successful meetings. Previous versions wereheld in Berkeley(1998), Nijmegen (1999), Pittsburgh(2000), Rome (2001), PaloAlto (2002), Prague(2003), Philadelphia (2004), Zurich (2005), Santa B- bara (2006), Pisa (2007), and St. Louis (2008). HSCC 2009 was part of the 2nd Cyber-Physical Systems Week (CPSWeek), whichconsistedoftheco-locationofHSCCwiththeInternationalConferenceon Information Processing in Sensor Networks (IPSN) and the Real-Time and - bedded Technology and Applications Symposium (RTAS). Through CPSWeek, the three conferences had joint invited speakers, poster sessions, and joint - cial events. In addition to the workshops sponsored by CPSWeek, HSCC 2009 sponsored two workshops: - NSV II: Second International Workshop on Numerical Software Veri?cation - HSCB 2009: Hybrid Systems Approaches to Computational Biology We would like to thank the authors of submitted papers, the Program C- mittee members, the additional reviewers, the workshop organizers, and the HSCC Steering Committee members for their help in composing a strong p- gram. We also thank the CPSWeek Organizing Committee, in particular Rajesh Gupta, for their strenuous work in handling the local arrangemen

Recent technological developments in sensing, communications, control and computation have created an emerging class of complex systems hereon called networked embedded systems. These systems can be roughly described as collections of spatially distributed sensors, actuators and controllers whose behaviour is coordinated through wired or wireless communication links. This integration between different technologies and scientific domains presents new and challenging fundamental problems underlying the theoretical foundations for this class of systems. This workshop aims at bringing together researchers working of different aspects of networked embedded systems in order to exchange research experiences and to identify the main scientific challenges in this exciting new area.