A Differential Operator Approach to Equational Differential Invariants

(Invited Paper)
  • André Platzer
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7406)


Hybrid systems, i.e., dynamical systems combining discrete and continuous dynamics, have a complete axiomatization in differential dynamic logic relative to differential equations. Differential invariants are a natural induction principle for proving properties of the remaining differential equations. We study the equational case of differential invariants using a differential operator view. We relate differential invariants to Lie’s seminal work and explain important structural properties resulting from this view. Finally, we study the connection of differential invariants with partial differential equations in the context of the inverse characteristic method for computing differential invariants.


Hybrid System Invariant Function Dynamic Logic Invariant Equation Differential Invariant 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • André Platzer
    • 1
  1. 1.Computer Science DepartmentCarnegie Mellon UniversityPittsburghUSA

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