Method of averaging for the system of functional-differential inclusions

Teresa Janiak; Elżbieta Łuczak-Kumorek

Discussiones Mathematicae, Differential Inclusions, Control and Optimization (1996)

  • Volume: 16, Issue: 2, page 137-151
  • ISSN: 1509-9407

Abstract

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The basic idea of this paper is to give the existence theorem and the method of averaging for the system of functional-differential inclusions of the form ⎧ ẋ ( t ) ∈ F ( t , x t , y t ) (0) ⎨ ⎩ ẋ ( t ) ∈ G ( t , x t , y t ) (1)

How to cite

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Teresa Janiak, and Elżbieta Łuczak-Kumorek. "Method of averaging for the system of functional-differential inclusions." Discussiones Mathematicae, Differential Inclusions, Control and Optimization 16.2 (1996): 137-151. <http://eudml.org/doc/275882>.

@article{TeresaJaniak1996,
abstract = {The basic idea of this paper is to give the existence theorem and the method of averaging for the system of functional-differential inclusions of the form ⎧$ẋ(t) ∈ F(t,x_t,y_t)$ (0) ⎨ ⎩$ẋ(t) ∈ G(t,x_t,y_t)$ (1)},
author = {Teresa Janiak, Elżbieta Łuczak-Kumorek},
journal = {Discussiones Mathematicae, Differential Inclusions, Control and Optimization},
keywords = {multifunctions; differential inclusions; functional-differential inclusions; averaging theorems},
language = {eng},
number = {2},
pages = {137-151},
title = {Method of averaging for the system of functional-differential inclusions},
url = {http://eudml.org/doc/275882},
volume = {16},
year = {1996},
}

TY - JOUR
AU - Teresa Janiak
AU - Elżbieta Łuczak-Kumorek
TI - Method of averaging for the system of functional-differential inclusions
JO - Discussiones Mathematicae, Differential Inclusions, Control and Optimization
PY - 1996
VL - 16
IS - 2
SP - 137
EP - 151
AB - The basic idea of this paper is to give the existence theorem and the method of averaging for the system of functional-differential inclusions of the form ⎧$ẋ(t) ∈ F(t,x_t,y_t)$ (0) ⎨ ⎩$ẋ(t) ∈ G(t,x_t,y_t)$ (1)
LA - eng
KW - multifunctions; differential inclusions; functional-differential inclusions; averaging theorems
UR - http://eudml.org/doc/275882
ER -

References

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  1. [1] N.N. Bogolubov, On some statistical methods in mathematical physics, Izv. Acad. Nauk USSR, Lwow 1945. 
  2. [2] M. Dawidowski, On some generalizations of Bogolubov averaging theorem, Funct. et Approx. 7 (1979), 55-70. Zbl0422.34013
  3. [3] A.F. Filippov, Classical solutions of differential equations with multivalued right-hand side, SIAM, J. Control 5 (1967), 609-621. 
  4. [4] M.M. Hapajev, O.P. Fiatov, O principie usrednijanija dla sistiem s bystrymi i miedljennymi opriemiennymi, Diff. Uravn. 19 (9) (1983), 1640-1643. 
  5. [5] T. Janiak, E. Łuczak-Kumorek, The theorem of middling for functional-differential equations neutral type, Discuss. Math. 11 (1991) 63-73. Zbl0754.34040
  6. [6] T. Janiak E. Łuczak-Kumorek, A theorem on partial middling for functional-differential equations of the neutral type, Review of research, Faculty of Science, Univ. of Novi Sad, Math. Series 16 (2) (1986). Zbl0651.34065
  7. [7] T. Janiak, E. uczak-Kumorek, Method of averaging for integral-differential inclusions, Studia Univ. Babes Bolyai, Math. 39 (2) 1994. 
  8. [8] S.S. Klimczuk, Averaging of differential inclusions with unbounded right-hand side, Ukr. Math. Zhurnal 3 (1989), 389-391 (Russian). 
  9. [9] W.A. Plotnikov, The averaging method for differential inclusions and his application in control theory, Diff. Uravn. 15 (8) (1979), 1427-1433 (Russian). 
  10. [10] W.A. Plotnikov, L. Mussa, Obosnowanie adnoj schemy czasticznowo usrednienia dla sistem z midliennymi i bystrymi pieriemiennymi, Diff. Uravn. 28 (4) (1992), 428-432. 

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