## Abstract

The paper is concerned with defining families of smooth functions that can be used for the approximation of impulsive types of solutions for linear systems. We review the different types of approximations of distributions in terms of smooth functions and explains their significance in the characterization of system properties where impulses were used for their characterisation. For controllable systems, we establish an interesting relation between the time t and sigma (volatility) in the approximation of distributional solutions. An algorithm is then proposed for the calculation of the coefficients of the input required to minimize the distance of our desired target state before and after approximation is proposed. The optimal choice of sigma is derived for a pre-determined time t for the state transition.

Original language | English |
---|---|

Title of host publication | 4th IFAC Symposium on System, Structure and Control, SSSC 2010 |

Pages | 115-122 |

Number of pages | 8 |

DOIs | |

Publication status | Published - 2010 |

Externally published | Yes |

Event | 4th IFAC Symposium on System, Structure and Control, SSSC 2010 - Ancona, Italy Duration: 15 Sep 2010 → 17 Sep 2010 |

### Conference

Conference | 4th IFAC Symposium on System, Structure and Control, SSSC 2010 |
---|---|

Country | Italy |

City | Ancona |

Period | 15/09/10 → 17/09/10 |

## Keywords

- Approximating distributional behaviour
- Gaussian function and its derivatives
- Linear systems