The admissible disturbance for discrete nonlinear perturbed controlled systems

M. Rachik, M. Lhous, A. Tridane

Research output: Contribution to journalArticlepeer-review


Consider the discrete perturbed controlled nonlinear system given by and the output function (xw(i + 1) = Axw(i) + f(ui + αi) + g(vi) Σrj = 1 βjihj (xw(i)) i ≥ 0, xw(0) = x0 + γ and the output function yw(i) = Cxw(i), i ≥ 0, where w = (γ, (αi)i≥0, (βi)i≥0), is a disturbance which disturbs the system. The disturbance w is said to be ε-admissible if ||yw(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 languageEnglish
Pages (from-to)759-782
Number of pages24
JournalRocky Mountain Journal of Mathematics
Issue number2
Publication statusPublished - 2004
Externally publishedYes


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

ASJC Scopus subject areas

  • General Mathematics


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