On the continuity property of L-P balls and an application

Guseinov K. G., Nazlipinar A. S.

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, cilt.335, sa.2, ss.1347-1359, 2007 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 335 Sayı: 2
  • Basım Tarihi: 2007
  • Doi Numarası: 10.1016/j.jmaa.2007.01.109
  • Dergi Adı: JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.1347-1359
  • Anahtar Kelimeler: L-p space, set-valued map, control system, attainable set, ATTAINABLE SETS, CONTROL-SYSTEMS, MINIMUM ENERGY, TIME
  • Anadolu Üniversitesi Adresli: Hayır

Özet

In this paper continuity properties of the set-valued map p -> B-p(mu(0)), p is an element of (1, +infinity), are considered where B-p (mu(0)) is the closed ball of the space L-p ([t(0), theta]; R-m) centered at the origin with radius mu(0). It is proved that the set-valued map p -> B-p(mu(0)), p is an element of (1, +infinity), is continuous. Applying obtained results, the attainable set of the nonlinear control system with integral constraint on the control is studied. The admissible control functions are chosen from B-p (mu(0)). It is shown that the attainable set of the system is continuous with respect to p. (c) 2007 Elsevier Inc. All rights reserved.