### Abstract

The paper describes a stability test applied to coupled parabolic partial differential equations. The PDE's describe the temperature distribution of composite structures with linear inner heat sources. The distributed transfer functions are developed based on the transmission matrix of each layer. To analyse the stability of the system we define a virtual feedback-loop. We give the virtual feedback transfer functions for different boundary conditions. Given an open-loop linear system (the virtual feedback-loop) we can apply the Nyquist stability test to determine the critical gains of the inner heat sources. The method described is easy to use and avoids numerical problems arising from locating the infinite number of system poles by numerical approximation.

Original language | English |
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Title of host publication | 9th Mediterranean Conference on Control and Automation: Book of abstracts |

Place of Publication | Zagreb, Croatia |

Publisher | KoREMA Secretariat |

Pages | 151-151 |

Number of pages | 4 |

ISBN (Print) | 953-6037-34-3 |

Publication status | Published - 27 Jun 2001 |

Event | 9th IEEE Mediterranean Conference on Control and Automation, MED 2001 - Hotel Excelsior, Dubrovnik, Croatia Duration: 27 Jun 2001 → 29 Jun 2001 Conference number: 9 |

### Conference

Conference | 9th IEEE Mediterranean Conference on Control and Automation, MED 2001 |
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Abbreviated title | MED |

Country | Croatia |

City | Dubrovnik |

Period | 27/06/01 → 29/06/01 |

### Keywords

- Distributed-parameter systems
- Nyquist stability test
- Partial differential equations

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## Cite this

Vajta, M. (2001). Stability test for a parabolic partial differential equation. In

*9th Mediterranean Conference on Control and Automation: Book of abstracts*(pp. 151-151). Zagreb, Croatia: KoREMA Secretariat.