## Hybrid SystemsRobert L. Grossman, Anil Nerode, Anders P. Ravn, Hans Rischel Hybrid systems are networks of interacting digital and analog devices. Control systems for inherently unstable aircraft and computer aided manufacturing are typical applications for hybrid systems, but due to the rapid development of processor and circuit technology modern cars and consumer electronics use software to control physical processes. The identifying characteristic of hybrid systems is that they incorporate both continuous components governed by differential equations and also digital components - digital computers, sensors, and actuators controlled by programs. This volume of invited refereed papers is inspired by a workshop on the Theory of Hybrid Systems, held at the Technical University, Lyngby, Denmark, in October 1992, and by a prior Hybrid Systems Workshop, held at Cornell University, USA, in June 1991, organized by R.L. Grossman and A. Nerode. Some papers are the final versions of papers presented at these workshops and some are invited papers from other researchers who were not able to attend these workshops. |

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### Contents

Grossman University of Illinois at Chicago | 1 |

Z Chaochen UNUIIST | 36 |

T A Henzinger Cornell University | 60 |

Copyright | |

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action actuator algebra algorithm analysis Antsaklis assertion assume automata behavior bialgebra boolean Cat and Mouse clock components Computer Science condition consider constraints continuous control law control theory defined denote described detection differential equations discrete domain Duration Calculus dynamical systems edge event example expressed fault finite flame formal formula function gas burner Hoare triples hybrid control system hybrid systems IEEE implementation initial input alphabet integration graphs interface internal control automaton interval interval temporal logic invariant invariant subspace join irreducibles Leak linear mathematical methods Mouse system open sets operators output parameters partition phase plant Pnueli predicate problem proof properties pump reachability real numbers represented requirements safety satisfies semantics sensor sequence signals small topology space specification symbols synchronous temporal logic theorem timer tion TLA+ trajectories true variables vector verification water level