Precompactness of the Set of Trajectories of the Controllable System Described by a Nonlinear Volterra Integral Equation

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Huseyin A., Huseyin N.

MATHEMATICAL MODELLING AND ANALYSIS, cilt.17, sa.5, ss.686-695, 2012 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 17 Sayı: 5
  • Basım Tarihi: 2012
  • Doi Numarası: 10.3846/13926292.2012.736088
  • Dergi Adı: MATHEMATICAL MODELLING AND ANALYSIS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.686-695
  • Anahtar Kelimeler: nonlinear Volterra integral equation, controllable system, integral constraint, set of trajectories
  • Anadolu Üniversitesi Adresli: Evet

Özet

In this paper the controllable system whose behaviour is described by a nonlinear Volterra integral equation, is studied. The set of admissible control functions is the closed ball of the space L-p (p > 1) with radius mu(0) and centered at the origin. It is shown that the set of trajectories of the system is a bounded and pre-compact subset of the space of continuous functions.