## Abstract

Consider the discrete perturbed controlled nonlinear system given by and the output function (x^{w}(i + 1) = Ax^{w}(i) + f(u_{i} + α_{i}) + g(v_{i}) Σ^{r}_{j = 1} β^{j}_{i}h_{j} (x^{w}(i)) i ≥ 0, x^{w}(0) = x_{0} + γ and the output function y^{w}(i) = Cx^{w}(i), i ≥ 0, where w = (γ, (α_{i})_{i≥0}, (β_{i})_{i≥0}), is a disturbance which disturbs the system. The disturbance w is said to be ε-admissible if ||y^{w}(i) - y^{(i)}|| ≤ e, for all i ≥ 0, where (y(i))_{i≥0} is the output signal corresponding to the uninfected controlled system. The set of all ε-admissible disturbances is the admissible set E(ε). The characterization of E(ε) is investigated and practical algorithms with numerical simulations are given. The admissible set E¯(ε) for discrete delayed systems is also considered.

Original language | English |
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Pages (from-to) | 759-782 |

Number of pages | 24 |

Journal | Rocky Mountain Journal of Mathematics |

Volume | 34 |

Issue number | 2 |

DOIs | |

Publication status | Published - 2004 |

Externally published | Yes |

## Keywords

- Admissibility
- Asymptotic stability
- Discrete delayed systems
- Discrete nonlinear systems
- Disturbances
- Observability

## ASJC Scopus subject areas

- General Mathematics