### Abstract

It is known that for single-input neutrally stable planar systems, there exists a class of saturated globally stabilizing linear state feedback control laws. The goal of this paper is to characterize the dynamic behavior for such a system under arbitrary locally stabilizing linear state feedback control laws. On the one hand, for the continuous-time case, we show that all locally stabilizing linear state feedback control laws are also globally stabilizing control laws. On the other hand, for the discrete-time case, we first show that this property does not hold by explicitly constructing nontrivial periodic solution for a particular system. We then show for an example that there exists more globally stabilizing linear state feedback control laws than well known ones in the literature.

Original language | Undefined |
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Title of host publication | Proceedings of the European Control Conference 2013 (ECC13) |

Publisher | OmniPress |

Pages | 2728-2733 |

Number of pages | 6 |

ISBN (Print) | 978-3-9524173-4-8 |

Publication status | Published - 2013 |

Event | 2013 European Control Conference, ECC 2013 - Zürich, Switzerland Duration: 17 Jul 2013 → 19 Jul 2013 |

### Publication series

Name | |
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Publisher | Omnipress |

### Conference

Conference | 2013 European Control Conference, ECC 2013 |
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Abbreviated title | ECC |

Country | Switzerland |

City | Zürich |

Period | 17/07/13 → 19/07/13 |

### Keywords

- EWI-23870
- METIS-300109
- IR-87576

## Cite this

Yang, T., Stoorvogel, A. A., Saberi, A., & Johansson, K. H. (2013). Further results on saturated globally stabilizing linear state feedback control laws for single-input neutrally stable planar systems. In

*Proceedings of the European Control Conference 2013 (ECC13)*(pp. 2728-2733). OmniPress.