Decompositional Construction of Lyapunov Functions for Hybrid Systems

  • Jens Oehlerking
  • Oliver Theel
Conference paper

DOI: 10.1007/978-3-642-00602-9_20

Part of the Lecture Notes in Computer Science book series (LNCS, volume 5469)
Cite this paper as:
Oehlerking J., Theel O. (2009) Decompositional Construction of Lyapunov Functions for Hybrid Systems. In: Majumdar R., Tabuada P. (eds) Hybrid Systems: Computation and Control. HSCC 2009. Lecture Notes in Computer Science, vol 5469. Springer, Berlin, Heidelberg

Abstract

In this paper, we present an automatable decompositional method for the computation of Lyapunov functions for hybrid systems with complex discrete state spaces. We use graph-based reasoning to decompose hybrid automata into subgraphs, for which we then solve semidefinite optimization problems to obtain local Lyapunov functions. These local computations are made in a way that ensures that the family of local Lyapunov functions forms a global Lyapunov function, proving asymptotic stability of the system. The main advantages over standard LMI methods are 1) improved numerical stability due to smaller optimization problems, 2) the possibility of incremental construction of stable hybrid automata and 3) easier diagnosis of unstable parts of the automaton in case no Lyapunov function can be found.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Jens Oehlerking
    • 1
  • Oliver Theel
    • 1
  1. 1.Department of Computer ScienceCarl von Ossietzky University of OldenburgOldenburgGermany

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