### Abstract

This paper presents a decision algorithm for the analysis of the stability of a class of planar switched linear systems, modeled by hybrid automata. The dynamics in each location of the hybrid automaton is assumed to be linear and asymptotically stable; the guards on the transitions are hyper planes in the state space. We show that for every pair of an ingoing and an outgoing transition related to a location, the exact gain in the norm of the vector induced by the dynamics in that location can be computed. These exact gains are used in defining a gain automaton which forms the basis of an algorithmic criterion to determine if a planar hybrid automaton is stable or not.

Original language | Undefined |
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Title of host publication | Proceedings of the 18th international symposium on mathematical theory of networks & systems |

Place of Publication | USA |

Publisher | SIAM |

Pages | 11 |

Number of pages | 11 |

ISBN (Print) | not assigned |

Publication status | Published - Aug 2008 |

### Publication series

Name | |
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Publisher | SIAM |

Number | 2008/16200 |

### Keywords

- EWI-14798
- METIS-255078
- IR-65267

## Cite this

Daws, C. F., Langerak, R., & Polderman, J. W. (2008). Decision algorithm for the stability of planar switching linear systems. In

*Proceedings of the 18th international symposium on mathematical theory of networks & systems*(pp. 11). USA: SIAM.