### Abstract

This paper considers input-to-state stability (ISS) analysis of discrete-time systems using
continuous Lyapunov functions. The contributions are as follows. Firstly, the existence of a continuous Lyapunov function is related to inherent input-to-state stability on compact sets with respect to both inner and outer perturbations. If the Lyapunov function is K8 - continuous, this result applies to unbounded sets as well. Secondly, continuous control Lyapunov functions are employed to construct input-to-state stabilizing control laws for discrete-time systems subject to bounded perturbations. The goal is to design a receding horizon control scheme that allows the optimization of the ISS gain along a closed-loop
trajectory.

Original language | English |
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Title of host publication | Proceedings of the UKACC International Conference on Control, 7-10 September 2010, Coventry, United Kingdom |

Place of Publication | London |

Publisher | Institution of Engineering and Technology (IET) |

Pages | 613-619 |

ISBN (Print) | 978-184600-0386 |

Publication status | Published - 2010 |

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## Cite this

Lazar, M., Heemels, W. P. M. H., & Teel, A. R. (2010). Further input-to-state stability subtleties for discrete-time systems. In

*Proceedings of the UKACC International Conference on Control, 7-10 September 2010, Coventry, United Kingdom*(pp. 613-619). London: Institution of Engineering and Technology (IET).