## Abstract

In this paper, we consider a class of Linear Time-Invariant (LTI) descriptor (regular) differential systems with distributed continuous delays and several types of (regular and irregular) inputs. This special class of differential systems are inherent in many real-life applications; we merely mention fluid dynamics, the modelling of multi-body mechanisms, the pricing procedure of actuarial portfolios of products and the problem of protein folding. By using some elements of matrix pencil theory, we decompose the main system into two subsystems (which are so-called fast and slow systems), whose solutions are obtained as generalized processes (in the sense of the Dirac delta distributions). Moreover, the form of the initial function is given, so the corresponding initial value problem is uniquely solvable. Finally, an illustrative application inspired by Insurance is briefly presented using standard Brownian motions.

Original language | English |
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Pages (from-to) | 31-38 |

Number of pages | 8 |

Journal | Systems Science |

Volume | 35 |

Issue number | 1 |

Publication status | Published - 2009 |

Externally published | Yes |

## Keywords

- Descriptor systems
- Distributed delays
- Insurance
- White noise (standard Brownian noise)