Computation of local ISS Lyapunov functions with low gains via linear programming

Huijuan Li, Robert Baier, Lars Grüne, Sigurdur F. Hafstein, Fabian R. Wirth

Research output: Contribution to journalArticlepeer-review

9 Citations (Scopus)


In this paper, we present a numerical algorithm for computing ISS Lyapunov functions for continuous-time systems which are input-to-state stable (ISS) on compact subsets of the state space. The algorithm relies on a linear programming problem and computes a continuous piecewise affine ISS Lyapunov function on a simplicial grid covering the given compact set excluding a small neighborhood of the origin. The objective of the linear programming problem is to minimize the gain. We show that for every ISS system with a locally Lipschitz right-hand side our algorithm is in principle able to deliver an ISS Lyapunov function. For C2 right-hand sides a more efficient algorithm is proposed.

Original languageEnglish
Pages (from-to)2477-2495
Number of pages19
JournalDiscrete and Continuous Dynamical Systems - Series B
Issue number8
Publication statusPublished - 1 Oct 2015

Bibliographical note

Publisher Copyright:
Copyright © DCDSB. 2015.

Other keywords

  • Linear programming
  • Local input-to-state stability
  • Local ISS Lyapunov function
  • Nonlinear systems
  • Robust Lyapunov function


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