Efficient Computation of Reachable Sets of Linear Time-Invariant Systems with Inputs

  • Antoine Girard
  • Colas Le Guernic
  • Oded Maler
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3927)


This work is concerned with the problem of computing the set of reachable states for linear time-invariant systems with bounded inputs. Our main contribution is a novel algorithm which improves significantly the computational complexity of reachability analysis. Algorithms to compute over and under-approximations of the reachable sets are proposed as well. These algorithms are not subject to the wrapping effect and therefore our approximations are tight. We show that these approximations are useful in the context of hybrid systems verification and control synthesis. The performance of a prototype implementation of the algorithm confirms its qualities and gives hope for scaling up verification technology for continuous and hybrid systems.


Hybrid System Recurrence Relation Memory Consumption Reachable State Reachability Analysis 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Antoine Girard
    • 1
  • Colas Le Guernic
    • 2
  • Oded Maler
    • 3
  1. 1.Department of Electrical and Systems EngineeringUniversity of PennsylvaniaPhiladelphiaUSA
  2. 2.École Normale SupérieureParisFrance
  3. 3.VERIMAGGièresFrance

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