## Reachability Analysis of Dynamical Systems having Piecewise-Constant Derivatives (1995)

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Venue: | Theoretical Computer Science |

Citations: | 110 - 18 self |

### BibTeX

@ARTICLE{Asarin95reachabilityanalysis,

author = {Eugene Asarin and Oded Maler and Amir Pnueli},

title = {Reachability Analysis of Dynamical Systems having Piecewise-Constant Derivatives},

journal = {Theoretical Computer Science},

year = {1995},

volume = {138},

pages = {35--66}

}

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### Abstract

In this paper we consider a class of hybrid systems, namely dynamical systems with piecewise-constant derivatives (PCD systems). Such systems consist of a partition of the Euclidean space into a finite set of polyhedral sets (regions). Within each region the dynamics is defined by a constant vector field, hence discrete transitions occur only on the boundaries between regions where the trajectories change their direction. With respect to such systems we investigate the reachability question: Given an effective description of the systems and of two polyhedral subsets P and Q of the state-space, is there a trajectory starting at some x 2 P and reaching some point in Q? Our main results are a decision procedure for two-dimensional systems, and an undecidability result for three or more dimensions. 1 Introduction 1.1 Motivation Hybrid systems (HS) are systems that combine intercommunicating discrete and continuous components. Most embedded systems belong to this class since they operate...

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