Reachability Analysis of Multi-affine Systems

  • Marius Kloetzer
  • Calin Belta
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3927)


We present a technique for reachability analysis of continuous multi-affine systems based on rectangular partitions. The method is iterative. At each step, finer partitions and larger discrete quotients are produced. We exploit some interesting convexity properties of multi-affine functions on rectangles to show that the construction of the discrete quotient at each step requires only the evaluation of the vector field at the set of all vertices of all rectangles in the partition and finding the roots of a finite set of scalar affine functions. The methodology promises to be easily extendable to rectangular hybrid automata with multi-affine vector fields and is expected to find important applications in analysis of biological networks and robot control.


Hybrid System Hybrid Automaton Reachability Analysis Initial Partition Reachability Problem 
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© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Marius Kloetzer
    • 1
  • Calin Belta
    • 1
  1. 1.Center for Information and Systems EngineeringBoston UniversityBrooklineUSA

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