Controllable systems of partial differential equations

František Tumajer

Aplikace matematiky (1986)

  • Volume: 31, Issue: 1, page 41-53
  • ISSN: 0862-7940

Abstract

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In the paper definitions of various kinds of stability and boundedness of solutions of linear controllable systems of partial differential equations are introduced and their interconnections are derived. By means of Ljapunov's functions theorems are proved which give necessary and sufficient conditions for particular kinds of stability and boundedness of the solutions.

How to cite

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Tumajer, František. "Controllable systems of partial differential equations." Aplikace matematiky 31.1 (1986): 41-53. <http://eudml.org/doc/15434>.

@article{Tumajer1986,
abstract = {In the paper definitions of various kinds of stability and boundedness of solutions of linear controllable systems of partial differential equations are introduced and their interconnections are derived. By means of Ljapunov's functions theorems are proved which give necessary and sufficient conditions for particular kinds of stability and boundedness of the solutions.},
author = {Tumajer, František},
journal = {Aplikace matematiky},
keywords = {stability; boundedness; controllable system of partial differential equations; Ljapunov's function; stability; boundedness; controllable system of partial differential equations},
language = {eng},
number = {1},
pages = {41-53},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Controllable systems of partial differential equations},
url = {http://eudml.org/doc/15434},
volume = {31},
year = {1986},
}

TY - JOUR
AU - Tumajer, František
TI - Controllable systems of partial differential equations
JO - Aplikace matematiky
PY - 1986
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 31
IS - 1
SP - 41
EP - 53
AB - In the paper definitions of various kinds of stability and boundedness of solutions of linear controllable systems of partial differential equations are introduced and their interconnections are derived. By means of Ljapunov's functions theorems are proved which give necessary and sufficient conditions for particular kinds of stability and boundedness of the solutions.
LA - eng
KW - stability; boundedness; controllable system of partial differential equations; Ljapunov's function; stability; boundedness; controllable system of partial differential equations
UR - http://eudml.org/doc/15434
ER -

References

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  1. H. П. Соколов, О функциях от многомерных матриц и примении их к решению линейных систем дифференциальных уравнений с частными производными, УМЖ, т. 22, No. 6, 1970, 769-782. (1970) Zbl1107.83313
  2. J. Kučera I. Vrkoč, Note on stability of a linear homogeneous control system, Časop. pěst. mat. 95 (1970), 56-61. (1970) Zbl0203.47702MR0277277
  3. F. Tumajer, Ljapunov's method in the theory of the boundedness of linear control flows, (Czech.) Časop. pěst. mat. 98 (1973), 278-284. (1973) Zbl0265.93021MR0326094

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