### Abstract

In this paper, we study the stability of periodic solutions of linear systems with state jump. Such a model arises, for example, when we consider the periodic motion of passive walkers [2]. In our previous work [4], we derived such a model by simplifying the result of Garcia et al.[6] and analyzed its stability via the Poincaré map. Also the effects of the feedback control strategies, OGY and DFC (Delayed Feedback Control) methods, were examined in the same framework. However, the Poincaré map was introduced rather ad-hoc manner there. In this paper, we refine the mathematical treatment of Poincaré map. After defining a special type of stability for the periodic solution considered here, we show that the stability via Poincaré map is equivalent to this specific definition. Also the effect of the data loss caused by the variation of the state jump interval in OGY case is examined.

Original language | English |
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Pages | 949-953 |

Number of pages | 5 |

Publication status | Published - Dec 1 2003 |

Externally published | Yes |

Event | Proceedings of 2003 IEEE Conference on Control Applications - Istanbul, Turkey Duration: Jun 23 2003 → Jun 25 2003 |

### Other

Other | Proceedings of 2003 IEEE Conference on Control Applications |
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Country | Turkey |

City | Istanbul |

Period | 6/23/03 → 6/25/03 |

### ASJC Scopus subject areas

- Control and Systems Engineering

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## Cite this

*Stability analysis of linear systems with state jump Motivated by periodic motion control of passive walker*. 949-953. Paper presented at Proceedings of 2003 IEEE Conference on Control Applications, Istanbul, Turkey.