### Abstract

In this paper, we introduce the class of semi-separable kernel functions for use in constructing Lyapunov functions for distributed-parameter systems such as delaydifferential equations. We then consider the subset of semiseparable kernel functions defined by polynomials. We show that the set of such kernels which define positive forms can be parameterized by positive semidefinite matrices. In the particular case of linear time-delay systems, we show how to construct the derivative of Lyapunov functions defined by piecewise continuous semi-separable kernels and give numerical examples which illustrate some advantages over standard polynomial kernel functions.

Original language | English (US) |
---|---|

Title of host publication | Proceedings of the 47th IEEE Conference on Decision and Control, CDC 2008 |

Pages | 847-852 |

Number of pages | 6 |

DOIs | |

State | Published - Dec 1 2008 |

Externally published | Yes |

Event | 47th IEEE Conference on Decision and Control, CDC 2008 - Cancun, Mexico Duration: Dec 9 2008 → Dec 11 2008 |

### Publication series

Name | Proceedings of the IEEE Conference on Decision and Control |
---|---|

ISSN (Print) | 0191-2216 |

### Other

Other | 47th IEEE Conference on Decision and Control, CDC 2008 |
---|---|

Country | Mexico |

City | Cancun |

Period | 12/9/08 → 12/11/08 |

### Fingerprint

### ASJC Scopus subject areas

- Control and Systems Engineering
- Modeling and Simulation
- Control and Optimization

### Cite this

*Proceedings of the 47th IEEE Conference on Decision and Control, CDC 2008*(pp. 847-852). [4739245] (Proceedings of the IEEE Conference on Decision and Control). https://doi.org/10.1109/CDC.2008.4739245