### Abstract

This paper considers the problem of computing a Lyapunov function for nonlinear discrete–time systems. The proposed solution is systematic and consists of two steps. First, a pseudo–Lyapunov function, called finite–step Lyapunov function, is computed by solving a finite dimensional nonlinear optimization problem. Then, a recent converse theorem is employed, which gives an explicit construction of a Lyapunov function from a finite–step Lyapunov function. This procedure produces additionally an invariant set, through a nonlinear optimization program. An example illustrates the developed procedure and gives insight into the problem complexity

Original language | English |
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Title of host publication | Proceedings of the 18th International Conference on System Theory, Control and Computing (ICSTCC) 17-19 October 2014, Sinaia, Romania |

Place of Publication | Piscataway |

Publisher | Institute of Electrical and Electronics Engineers |

Pages | 93-98 |

DOIs | |

Publication status | Published - 2014 |

Event | 18th International Conference on System Theory, Control and Computing (ICSTCC 2014), October 17-19, 2014, Sinaia, Romania - Sinaia, Romania Duration: 17 Oct 2014 → 19 Oct 2014 |

### Conference

Conference | 18th International Conference on System Theory, Control and Computing (ICSTCC 2014), October 17-19, 2014, Sinaia, Romania |
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Abbreviated title | ICSTCC 2014 |

Country | Romania |

City | Sinaia |

Period | 17/10/14 → 19/10/14 |

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## Cite this

Bobiti, R. V., & Lazar, M. (2014). On the computation of Lyapunov functions for discrete–time nonlinear systems. In

*Proceedings of the 18th International Conference on System Theory, Control and Computing (ICSTCC) 17-19 October 2014, Sinaia, Romania*(pp. 93-98). Institute of Electrical and Electronics Engineers. https://doi.org/10.1109/ICSTCC.2014.6982397