Title | ABSOLUTE AND INPUT-TO-STATE STABILITIES OF NONAUTONOMOUS SYSTEMS WITH CAUSAL MAPPINGS |

Publication Type | Journal Article |

Year of Publication | 2009 |

Authors | GIL MICHAEL |

Journal | Dynamic Systems and Applications |

Volume | 18 |

Start Page | 655 |

Pagination | 12 |

Date Published | 2009 |

ISSN | 1056-2176 |

AMS Subject Classification | 34K20, 34K99, 93D05, 93D25 |

Abstract | We consider systems governed by the scalar equation Xn k=0 ak(t)x (n−k) (t) = [Fx](t) (t ≥ 0), where a0 ≡ 1; ak(t) (k = 1, . . ., n) are positive continuous functions and F is a causal mapping. We also consider the case when F depends on the input. Such equations include differential, integrodifferential and other traditional equations. It is assumed that all the roots rk(t) (k = 1, . . ., n) of the polynomial z n + a1(t)z n−1 + · · · + an(t) are real and negative for all t ≥ 0. Exact explicit conditions for the absolute and input-to-state stabilities of the considered systems are established. |

https://acadsol.eu/dsa/articles/18/43-DSA-210.pdf | |

Refereed Designation | Refereed |